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tomleslie

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These are answers submitted by tomleslie

Maybe timelimit()...

tomleslie 13876
September 03 2022
1 0

from the help page:

timelimit(t, x)

The timelimit function evaluates the expression x, but gives up if the evaluation takes longer than the number of seconds specified by t.

Thiu will generate an error if the timelimit is exceeded.You will have to "trap" this using and appropriate try..catch construct to ensure that your loop will keep executing afetr the error.

Hmmmm...

tomleslie 13876
August 30 2022
0 3

DPI would "normally" be considered a property of the monitor on which you are displaying the plot.

Perhaps you are referring to the number of points at which the function [x, f(x)] is evaluate? If so, check the plot option numpoints. From the help page for the plot,options command (available by entering ?plot,options at the command prompt), one can read

numpoints=n
Specifies the minimum number of points to be generated.  The default is "200".
Note: plot employs an adaptive plotting scheme which automatically does more work where the function values do not lie close to a straight line.  Hence, plot often generates more than the minimum number of points.

 

Product Graphs...

tomleslie 13876
August 30 2022
0 0

In the attached I have provided code for each of the product graphs listed on

https://en.wikipedia.org/wiki/Graph_product

where the logical conditions are given in the "overview Table" of the above article.

I have written a procedure for each of the product graphs separately. These procedures only differ in the logical condition specified in the 'if' clause. The logical conditions used are lifted directly from the second column of the "Overview Table" in the above Wikipedia page.

See further comments in the attached.

> 

  restart:
  with(GraphTheory):
  with(RandomGraphs):
  with(StringTools):
#
# A couple of random graphs for test purposes
#
  G1:= RandomGraph(6,10);
  G2:= RandomGraph(7,12);
#
# Generate all the vertices for the product graph
#
  vertexList:=[ seq
                ( seq
                  ( Join
                    ( [i, ":", j]
                    ),
                    i in convert~(Vertices(G1), string)
                  ),
                  j in convert~(Vertices(G2), string)
                )
              ]:
  coNorm:= proc( verts::list)
                 uses StringTools, GraphTheory:
                 local e1:= parse~( Split(verts[1], ":") ),
                       a1:= e1[1],
                       a2:= e1[2],
                       e2:= parse~( Split(verts[2], ":") ),
                       b1:= e2[1],
                       b2:= e2[2]:
                 if  `or`( HasEdge(G1, {a1, b1}),  HasEdge(G2, {a2, b2}))
                 then AddEdge(G3, {verts[1], verts[2]}):
                 fi;
           end proc:

  cartProd:= proc( verts::list)
                   uses StringTools, GraphTheory:
                   local e1:= parse~( Split(verts[1], ":") ),
                         a1:= e1[1],
                         a2:= e1[2],
                         e2:= parse~( Split(verts[2], ":") ),
                         b1:= e2[1],
                         b2:= e2[2]:
                   if  `or`( `and`( a1=b1, HasEdge(G2, {a2, b2})),
                             `and`( HasEdge(G1, {a1, b1}), a2=b2)
                           )
                   then AddEdge(G3, {verts[1], verts[2]}):
                   fi;
             end proc:
  tensProd:= proc( verts::list)
                   uses StringTools, GraphTheory:
                   local e1:= parse~( Split(verts[1], ":") ),
                         a1:= e1[1],
                         a2:= e1[2],
                         e2:= parse~( Split(verts[2], ":") ),
                         b1:= e2[1],
                         b2:= e2[2]:
                   if  `and`( HasEdge(G1, {a1, b1}), HasEdge(G2, {a2, b2}))
                   then AddEdge(G3, {verts[1], verts[2]}):
                   fi;
             end proc:
  lexiProd:= proc( verts::list)
                   uses StringTools, GraphTheory:
                   local e1:= parse~( Split(verts[1], ":") ),
                         a1:= e1[1],
                         a2:= e1[2],
                         e2:= parse~( Split(verts[2], ":") ),
                         b1:= e2[1],
                         b2:= e2[2]:
                   if  `or`( HasEdge(G1, {a1, b1}),
                             `and`( a1=b1, HasEdge(G2, {a2, b2}))
                           )
                   then AddEdge(G3, {verts[1], verts[2]}):
                   fi;
             end proc:
  strongProd:= proc( verts::list)
                     uses StringTools, GraphTheory:
                     local e1:= parse~( Split(verts[1], ":") ),
                           a1:= e1[1],
                           a2:= e1[2],
                           e2:= parse~( Split(verts[2], ":") ),
                           b1:= e2[1],
                           b2:= e2[2]:
                     if  `or`( `and`( a1=b1, HasEdge(G2, {a2, b2})),
                               `and`( HasEdge(G1, {a1, b1}), a2=b2),
                               `and`(HasEdge(G1, {a1, b1}), HasEdge(G2, {a2, b2}))
                             )
                     then AddEdge(G3, {verts[1], verts[2]}):
                     fi;
             end proc:
  moduProd:= proc( verts::list)
                   uses StringTools, GraphTheory:
                   local e1:= parse~( Split(verts[1], ":") ),
                         a1:= e1[1],
                         a2:= e1[2],
                         e2:= parse~( Split(verts[2], ":") ),
                         b1:= e2[1],
                         b2:= e2[2]:
                   if  `or`( `and`( HasEdge(G1, {a1, b1}), HasEdge(G2, {a2, b2})),
                             `and`( not HasEdge(G1, {a1, b1}), HasEdge(G2, {a2, b2}))
                           )
                   then AddEdge(G3, {verts[1], verts[2]}):
                   fi:
             end proc:
  homoProd:= proc( verts::list)
                   uses StringTools, GraphTheory:
                   local e1:= parse~( Split(verts[1], ":") ),
                         a1:= e1[1],
                         a2:= e1[2],
                         e2:= parse~( Split(verts[2], ":") ),
                         b1:= e2[1],
                         b2:= e2[2]:
                   if  `or`(  a1=b1,
                             `and`( HasEdge(G1, {a1, b1}), not HasEdge(G2, {a2, b2}))
                           )
                   then AddEdge(G3, {verts[1], verts[2]}):
                   fi:
             end proc:

GRAPHLN(undirected, unweighted, [1, 2, 3, 4, 5, 6], Array(1..6, {(1) = {2, 3, 4, 5}, (2) = {1, 3, 6}, (3) = {1, 2, 4}, (4) = {1, 3, 5, 6}, (5) = {1, 4, 6}, (6) = {2, 4, 5}}), `GRAPHLN/table/2`, 0)

  

GRAPHLN(undirected, unweighted, [1, 2, 3, 4, 5, 6, 7], Array(1..7, {(1) = {3, 5, 6}, (2) = {3, 4, 7}, (3) = {1, 2, 6, 7}, (4) = {2, 6, 7}, (5) = {1, 6}, (6) = {1, 3, 4, 5, 7}, (7) = {2, 3, 4, 6}}), `GRAPHLN/table/4`, 0)

 (1)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the conormal product graph G3
#
  coNorm~(combinat:-choose(Vertices(G3), 2) ):
#
# Check that the edge count in the product
# graph corresponds with that given in
# https://en.wikipedia.org/wiki/Graph_product
#
  is( numelems(Edges(G3)) = numelems( Vertices(G1))^2*numelems(Edges(G2))
                            +
                            numelems( Vertices(G2))^2*numelems(Edges(G1))
                            -
                            2*numelems(Edges(G2))*numelems(Edges(G1))
    );

true

 (2)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the cartesian product graph G3. NB MAple already
# has a command for this, so this execution group is only
# here for illustration
#
  cartProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Check that the edge count in the product
# graph corresponds with that given in
# https://en.wikipedia.org/wiki/Graph_product
#
  is( numelems(Edges(G3))= numelems( Edges( CartesianProduct(G1, G2)))
    );

true

 (3)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the tensor product graph G3.
#
  tensProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Check that the edge count in the product
# graph corresponds with that given in
# https://en.wikipedia.org/wiki/Graph_product
#
  is( numelems(Edges(G3))= 2*numelems(Edges(G1))*numelems(Edges(G2))
    );

true

 (4)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the lexicographic product graph G3.
#
  lexiProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Check that the edge count in the product
# graph corresponds with that given in
# https://en.wikipedia.org/wiki/Graph_product
#
  is( numelems(Edges(G3))= numelems(Vertices(G1))*numelems(Edges(G2))
                           +
                           numelems(Edges(G1))*numelems(Vertices(G2))^2
    );

true

 (5)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the strong product graph G3.
#
  strongProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Check that the edge count in the product
# graph corresponds with that given in
# https://en.wikipedia.org/wiki/Graph_product
#
  is( numelems(Edges(G3))= numelems(Vertices(G1))*numelems(Edges(G2))
                           +
                           numelems(Vertices(G2))*numelems(Edges(G1))
                           +
                           2*numelems(Edges(G1))*numelems(Edges(G2))
    );

true

 (6)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the modular product graph G3.
#
  moduProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Don't know how many edges this should have" No
# formula given in
# https://en.wikipedia.org/wiki/Graph_product
#
  G3;

GRAPHLN(undirected, unweighted, ["1 : 1", "2 : 1", "3 : 1", "4 : 1", "5 : 1", "6 : 1", "1 : 2", "2 : 2", "3 : 2", "4 : 2", "5 : 2", "6 : 2", "1 : 3", "2 : 3", "3 : 3", "4 : 3", "5 : 3", "6 : 3", "1 : 4", "2 : 4", "3 : 4", "4 : 4", "5 : 4", "6 : 4", "1 : 5", "2 : 5", "3 : 5", "4 : 5", "5 : 5", "6 : 5", "1 : 6", "2 : 6", "3 : 6", "4 : 6", "5 : 6", "6 : 6", "1 : 7", "2 : 7", "3 : 7", "4 : 7", "5 : 7", "6 : 7"], Array(1..42, {(1) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (2) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (3) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (4) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (5) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (6) = {13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}, (7) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (8) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (9) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (10) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (11) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (12) = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 37, 38, 39, 40, 41, 42}, (13) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (14) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (15) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (16) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (17) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (18) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (19) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (20) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (21) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (22) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (23) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (24) = {7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}, (25) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (26) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (27) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (28) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (29) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (30) = {1, 2, 3, 4, 5, 6, 31, 32, 33, 34, 35, 36}, (31) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (32) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (33) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (34) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (35) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (36) = {1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42}, (37) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}, (38) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}, (39) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}, (40) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}, (41) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}, (42) = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36}}), `GRAPHLN/table/11`, 0)

 (7)
> 

#
# Initialise the product graph
#
  G3:=Graph(vertexList):
#
# Compute the homomorphic product graph G3.
#
  homoProd~(combinat:-choose(Vertices(G3), 2) ):
#
# Don't know how many edges this should have" No
# formula given in
# https://en.wikipedia.org/wiki/Graph_product
#
  G3;

GRAPHLN(undirected, unweighted, ["1 : 1", "2 : 1", "3 : 1", "4 : 1", "5 : 1", "6 : 1", "1 : 2", "2 : 2", "3 : 2", "4 : 2", "5 : 2", "6 : 2", "1 : 3", "2 : 3", "3 : 3", "4 : 3", "5 : 3", "6 : 3", "1 : 4", "2 : 4", "3 : 4", "4 : 4", "5 : 4", "6 : 4", "1 : 5", "2 : 5", "3 : 5", "4 : 5", "5 : 5", "6 : 5", "1 : 6", "2 : 6", "3 : 6", "4 : 6", "5 : 6", "6 : 6", "1 : 7", "2 : 7", "3 : 7", "4 : 7", "5 : 7", "6 : 7"], Array(1..42, {(1) = {2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 19, 20, 21, 22, 23, 25, 31, 37, 38, 39, 40, 41}, (2) = {1, 3, 6, 7, 8, 9, 12, 14, 19, 20, 21, 24, 26, 32, 37, 38, 39, 42}, (3) = {1, 2, 4, 7, 8, 9, 10, 15, 19, 20, 21, 22, 27, 33, 37, 38, 39, 40}, (4) = {1, 3, 5, 6, 7, 9, 10, 11, 12, 16, 19, 21, 22, 23, 24, 28, 34, 37, 39, 40, 41, 42}, (5) = {1, 4, 6, 7, 10, 11, 12, 17, 19, 22, 23, 24, 29, 35, 37, 40, 41, 42}, (6) = {2, 4, 5, 8, 10, 11, 12, 18, 20, 22, 23, 24, 30, 36, 38, 40, 41, 42}, (7) = {1, 2, 3, 4, 5, 8, 9, 10, 11, 13, 19, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37}, (8) = {1, 2, 3, 6, 7, 9, 12, 14, 20, 25, 26, 27, 30, 31, 32, 33, 36, 38}, (9) = {1, 2, 3, 4, 7, 8, 10, 15, 21, 25, 26, 27, 28, 31, 32, 33, 34, 39}, (10) = {1, 3, 4, 5, 6, 7, 9, 11, 12, 16, 22, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 40}, (11) = {1, 4, 5, 6, 7, 10, 12, 17, 23, 25, 28, 29, 30, 31, 34, 35, 36, 41}, (12) = {2, 4, 5, 6, 8, 10, 11, 18, 24, 26, 28, 29, 30, 32, 34, 35, 36, 42}, (13) = {1, 7, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 37}, (14) = {2, 8, 13, 15, 18, 19, 20, 21, 24, 25, 26, 27, 30, 32, 38}, (15) = {3, 9, 13, 14, 16, 19, 20, 21, 22, 25, 26, 27, 28, 33, 39}, (16) = {4, 10, 13, 15, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 34, 40}, (17) = {5, 11, 13, 16, 18, 19, 22, 23, 24, 25, 28, 29, 30, 35, 41}, (18) = {6, 12, 14, 16, 17, 20, 22, 23, 24, 26, 28, 29, 30, 36, 42}, (19) = {1, 2, 3, 4, 5, 7, 13, 14, 15, 16, 17, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 37}, (20) = {1, 2, 3, 6, 8, 13, 14, 15, 18, 19, 21, 24, 25, 26, 27, 30, 32, 38}, (21) = {1, 2, 3, 4, 9, 13, 14, 15, 16, 19, 20, 22, 25, 26, 27, 28, 33, 39}, (22) = {1, 3, 4, 5, 6, 10, 13, 15, 16, 17, 18, 19, 21, 23, 24, 25, 27, 28, 29, 30, 34, 40}, (23) = {1, 4, 5, 6, 11, 13, 16, 17, 18, 19, 22, 24, 25, 28, 29, 30, 35, 41}, (24) = {2, 4, 5, 6, 12, 14, 16, 17, 18, 20, 22, 23, 26, 28, 29, 30, 36, 42}, (25) = {1, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 27, 28, 29, 31, 37, 38, 39, 40, 41}, (26) = {2, 7, 8, 9, 12, 13, 14, 15, 18, 19, 20, 21, 24, 25, 27, 30, 32, 37, 38, 39, 42}, (27) = {3, 7, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 22, 25, 26, 28, 33, 37, 38, 39, 40}, (28) = {4, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 29, 30, 34, 37, 39, 40, 41, 42}, (29) = {5, 7, 10, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 25, 28, 30, 35, 37, 40, 41, 42}, (30) = {6, 8, 10, 11, 12, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 29, 36, 38, 40, 41, 42}, (31) = {1, 7, 8, 9, 10, 11, 13, 19, 25, 32, 33, 34, 35, 37}, (32) = {2, 7, 8, 9, 12, 14, 20, 26, 31, 33, 36, 38}, (33) = {3, 7, 8, 9, 10, 15, 21, 27, 31, 32, 34, 39}, (34) = {4, 7, 9, 10, 11, 12, 16, 22, 28, 31, 33, 35, 36, 40}, (35) = {5, 7, 10, 11, 12, 17, 23, 29, 31, 34, 36, 41}, (36) = {6, 8, 10, 11, 12, 18, 24, 30, 32, 34, 35, 42}, (37) = {1, 2, 3, 4, 5, 7, 13, 19, 25, 26, 27, 28, 29, 31, 38, 39, 40, 41}, (38) = {1, 2, 3, 6, 8, 14, 20, 25, 26, 27, 30, 32, 37, 39, 42}, (39) = {1, 2, 3, 4, 9, 15, 21, 25, 26, 27, 28, 33, 37, 38, 40}, (40) = {1, 3, 4, 5, 6, 10, 16, 22, 25, 27, 28, 29, 30, 34, 37, 39, 41, 42}, (41) = {1, 4, 5, 6, 11, 17, 23, 25, 28, 29, 30, 35, 37, 40, 42}, (42) = {2, 4, 5, 6, 12, 18, 24, 26, 28, 29, 30, 36, 38, 40, 41}}), `GRAPHLN/table/12`, 0)

 (8)
> 

 

Download productGraphs.mw

Several ways...

tomleslie 13876
August 30 2022
0 0

One of the easiest is (probably) to use the plotttools:-transform() command to interchange 'x' and 'y', as shown in the attached.

> 

restart
> 

NULL
> 

y := 3*x^2-4*x+5

3*x^2-4*x+5

 (1)
> 

p1 := plot(y, x, axes = box, labels = ["x", "y"])

 
> 

t1 := plottools:-transform(proc (x, y) options operator, arrow; [y, x] end proc); plots:-display(t1(p1))

 
> 

 

Download transplot.mw

Check the halp at...

tomleslie 13876
August 29 2022
0 0

?Deep Learning.

I have never attempted to use this package, and have no knowledge of Google's "Tensorflow" software, so I have no idea how useful this might be. So far as I can tell, the DeepLearning() package is essentially a Maple "interface" to Google TensorFlow software, so I suspect that one would haave to be reasonably knowledgeable about the latter, before using the former

Assuming...

tomleslie 13876
August 29 2022
1 1

that by

  1. "long integer representing the ticks in JS", you mean an integer which represents time in units of 10-7 seconds, and by
  2. "convert them to a date in maple", you mean with respect to the "start time" of 00.00am on January 1, 1970 (UTC)

then the attached should fulfil the requirement.

Depending on your local time zone and default date format, the resulting date output may be different.

> 

  restart;
  JStickToDate:= proc( nT::integer, startDate:=Date( 1970, 1, 1, 0, 0, timezone="UTC" ) )
                       uses Calendar:
                       local nD:= trunc( nT/24/60/60/10^7 ),
                             nH:= trunc( (nT-nD*24*60*60*10^7 )/60/60/10^7 ),
                             nM:= trunc( (nT-(nD*24+nH)*60*60*10^7)/60/10^7 ),
                             nS:= trunc( (nT-((nD*24+nH)*60+nM)*60*10^7)/10^7 ):
                       return AdjustDateField
                              ( AdjustDateField
                                ( AdjustDateField
                                  ( AdjustDateField
                                    ( startDate,
                                      "day_of_month",
                                      nD
                                    ),
                                    "hour",
                                    nH
                                  ),
                                  "minute",
                                  nM
                                ),
                                "second",
                                nS
                              );
                 end proc:
#
# Usage: first argument is number of ticks;
#        (optional) second argument is start date
#
  JStickToDate(12345678901234567);
  JStickToDate(13345678901234567);
  JStickToDate(14345678901234567);

_m615572320

  

_m725718304

  

_m725342496

 (1)
> 

 

Download TickToDate.mw

 

 

I think that...

tomleslie 13876
August 28 2022
1 0

the attached is a bit simpler and neater

> 

  restart:
  with(plots):
  with(plottools):
  with(NumberTheory):
  randomize():
  rnge:=100:
  n:=rand(1..rnge)():
  m:=rand(n+1..rnge+n+1)():
#
# Check whether "triple" is primitive or not
# and set plot options appropriately
#
  if  `and`
       ( AreCoprime(m,n),
         `or`
          ( type(m, even),
            type(n, even)
          )
       )
  then cl:= red:
       tl:= "Primitive Pythagorean Triple":
  else cl:= blue:
       tl:= "Pythagorean Triple":
  fi:
#
# Get sidelengths
#
  a:=m^2-n^2:
  b:=2*m*n:
  c:=m^2+n^2:

  display( [ polygon( [[0, 0], [0, a], [b, 0]],
                      color=cl
                    ),
             textplot( [ [ 0,   a/2, "a", 'align'={'left'}],
                         [ b/2, 0,   "b", 'align'={'below'}],
                         [ b/2, a/2, "c", 'align'={'above', 'right'}]
                      ],
                      font= [times, bold, 16]
                    )
           ],
           title=tl,
           titlefont=[times, bold, 20],
           axes=none
         );
  

 
> 

 


 

Download pyTrip.mw

Evaluation rules...

tomleslie 13876
August 28 2022
3 3

cat() does not evaluate what it concatenates. From the help page for cat() - emphasis added

The cat function is commonly used to concatenate strings and names together. The arguments are concatenated to form either a string, a name, or an object of type `||` .

So you need an "extra" eval() command, as in the attached

Example: Assume expressions assigned to names

xa, xb, xc := y = x, y = x^2, x = x^3

y = x, y = x^2, x = x^3

 (1)

where you want to apply a command (rhs in this example) to all names fitting to a certain scheme (here a and c)

seq(cat(x, i), i = [a, c])

xa, xc

 (2)

`~`[rhs]([xa, xc])[]

x, x^3

 (3)

Combining (2) and (3) in one line

seq(rhs(eval(cat(x, i))), i = [a, c])

x, x^3

 (4)

 

NULL

Download catEval.mw

Well...

tomleslie 13876
August 28 2022
0 1

You can use

simplify(expr, zero)

as shiown in the final execution group of the attached - but I don't see anywhere in yur code whihc produces

I want to  return {x = 0., y = 1.158748796 + 0. I}  as  {x = 0., y = 1.158748796 }. 

When I check the output of

soln3:= fsolve({b1, b2}, {x = 0 .. infinity, y = 0 .. infinity});
soln4:= fsolve({b1, b2}, {x = -infinity ..0, y = -infinity .. 0}); 

both are producing {x = 0., y = 0.} ??????

> 

restart:

doCalc:= proc( xi )

                 # Import Packages
                 uses ArrayTools, Student:-Calculus1, LinearAlgebra,
                      ListTools, RootFinding, plots, ListTools:
                 local gamma__1:= .1093,
                       alpha__3:= -0.1104e-2,
                       k__1:= 6*10^(-12),
                       d:= 0.2e-3,
                       theta0:= 0.0001,
                       eta__1:= 0.240e-1,
                       alpha:= 1-alpha__3^2/(gamma__1*eta__1),
                       c:= alpha__3*xi*alpha/(eta__1*(4*k__1*q^2/d^2-alpha__3*xi/eta__1)),
                       theta_init:= theta0*sin(Pi*z/d),
                       n:= 30,
                       g, f, b1, b2, qstar, OddAsymptotes, ModifiedOddAsym,
                       qstarTemporary, indexOfqstar2, qstar2, AreThereComplexRoots,
                       soln1, soln2, qcomplex1, qcomplex2, gg, qq, m, pp, j, i,
                       AllAsymptotes, p, Efun, b, aa, F, A, B, Ainv, r, theta_sol, v, Vfun, v_sol,minp,nstar,
                       soln3, soln4, Imagroot1, Imagroot2;

# Assign g for q and plot g, Set q as a complex and Compute the Special Asymptotes

  g:= q-(1-alpha)*tan(q)+ c*tan(q):
  f:= subs(q = x+I*y, g):
  b1:= evalc(Re(f)) = 0:
  b2:= y-(1-alpha)*tanh(y) -(alpha__3*xi*alpha/(eta__1*(4*k__1*y^2/d^2+alpha__3*xi/eta__1)))*tanh(y) = 0:
  qstar:= (fsolve(1/c = 0, q = 0 .. infinity)):
  OddAsymptotes:= Vector[row]([seq(evalf(1/2*(2*j + 1)*Pi), j = 0 .. n)]);

# Compute Odd asymptote

  ModifiedOddAsym:= abs(`-`~(OddAsymptotes, qstar));
  qstarTemporary:= min(ModifiedOddAsym);
  indexOfqstar2:= SearchAll(qstarTemporary, ModifiedOddAsym);
  qstar2:= OddAsymptotes(indexOfqstar2);

# Compute complex roots

  AreThereComplexRoots:= type(true, 'truefalse');
  try
   soln1:= fsolve({b1, b2}, {x = min(qstar2, qstar) .. max(qstar2, qstar), y = 0 .. infinity});
   soln2:= fsolve({b1, b2}, {x = min(qstar2, qstar) .. max(qstar2, qstar), y = -infinity .. 0});
   qcomplex1:= subs(soln1, x+I*y);
   qcomplex2:= subs(soln2, x+I*y);
   catch:
   AreThereComplexRoots:= type(FAIL, 'truefalse');
  end try;

# Compute the rest of the Roots
  soln3:= fsolve({b1, b2}, {x = 0 .. infinity, y = 0 .. 10});
  printf("%a\n", soln3);
  soln4:= fsolve({b1, b2}, {x = -infinity ..0, y = -infinity .. 0});
  printf("%a\n", soln4);
  Imagroot1:=subs(soln3, I*y);
  Imagroot2:= subs(soln4, I*y);
  OddAsymptotes:= Vector[row]([seq(evalf((1/2)*(2*j+1)*Pi), j = 0 .. n)]);
  AllAsymptotes:= sort(Vector[row]([OddAsymptotes, qstar]));

  if AreThereComplexRoots
  then gg:= [qcomplex1, qcomplex2,op(Roots(g, q = 0.1e-3 .. AllAsymptotes[1])),
              seq(op(Roots(g, q = AllAsymptotes[i] .. AllAsymptotes[i+1])), i = 1 .. n)];
  elif not AreThereComplexRoots
  then gg:= [op(Roots(g, q = 0.1e-3 .. AllAsymptotes[1])), seq(op(Roots(g, q = AllAsymptotes[i] .. AllAsymptotes[i+1])), i = 1 .. n)];
  end if:

# Remove the repeated roots if any & Redefine n

  qq:= MakeUnique(gg):
  m:= numelems(qq):

## Return all the plots
            return qq, Imagroot1,Imagroot2, p, soln3, soln4;
  end proc:

ans:=[doCalc(0.06)];

{x = 0., y = 0.}
{x = 0., y = 0.}

  

[[4.675134212, 7.845062056, 10.99219719, 14.13554284, 17.27785480, 20.41979538, 23.56157656, 26.70328023, 29.84494257, 32.98658122, 36.12820550, 39.26982064, 42.41142975, 45.55303474, 48.69463685, 51.83623687, 54.97783536, 58.11943271, 61.26102919, 64.40262499, 67.54422027, 70.68581513, 73.82740965, 76.96900390, 80.11059793, 83.25219178, 86.39378547, 89.53537904, 92.67697249, 95.81856586], 0.*I, 0.*I, p, {x = 0., y = 0.}, {x = 0., y = 0.}]

 (1)
> 

a:={ 2+0.*I, 3 +0.*I};
simplify~(a, zero);

{2.+0.*I, 3.+0.*I}

  

{2., 3.}

 (2)
> 

 

Download oddProc3.mw

Well...

tomleslie 13876
August 28 2022
0 0

now uo are creating a table called 'w' and there are "special" considerations when return (potentially large) data structures - I' probably be using

return eval(w);

as in the attached

> 

restart:

doCalc:= proc( xi )

                 # Import Packages
                 uses ArrayTools, Student:-Calculus1, LinearAlgebra,
                      ListTools, RootFinding, plots, ListTools:
                 local gamma__1:= .1093,
                       alpha__3:= -0.1104e-2,
                       k__1:= 6*10^(-12),
                       d:= 0.2e-3,
                       theta0:= 0.0001,
                       eta__1:= 0.240e-1,
                       alpha:= 1-alpha__3^2/(gamma__1*eta__1),
                       c:= alpha__3*xi*alpha/(eta__1*(4*k__1*q^2/d^2-alpha__3*xi/eta__1)),
                       theta_init:= theta0*sin(Pi*z/d),
                       n:= 30,
                       g, f, b1, b2, qstar, OddAsymptotes, ModifiedOddAsym,
                       qstarTemporary, indexOfqstar2, qstar2, AreThereComplexRoots,
                       soln1, soln2, qcomplex1, qcomplex2, gg, qq, m, pp, j, i,
                       AllAsymptotes, w, Efun, b, aa, F, A, B, Ainv, r, theta_sol, v, Vfun, v_sol,minp,nstar,
                       soln3, soln4, Imagroot1, Imagroot2;

# Assign g for q and plot g, Set q as a complex and Compute the Special Asymptotes

                       qq := [2.106333379+.6286420119*I, 2.106333379-.6286420119*I, 4.654463885, 7.843624703, 10.99193295,14.13546782, 17.27782732, 20.41978346, 23.56157073, 26.70327712, 29.84494078, 32.98658013,         36.12820481, 39.26982019, 42.41142944, 45.55303453, 48.69463669, 51.83623675, 54.97783528,                     58.11943264, 61.26102914, 64.40262495, 67.54422024, 70.68581510, 73.82740963,                                 76.96900389, 80.11059792, 83.25219177, 86.39378546, 89.53537903, 92.67697249];
                        m:= numelems(qq):

                        for i from 1 to m do
                        w[i] := gamma__1*alpha/(4*k__1*qq[i]^2/d^2-alpha__3*xi/eta__1);
                        end do;

## Return all the plots
  return eval(w);
  end proc:

ans:=doCalc(0.06);
ans[1];
ans[3];

table( [( 1 ) = 19.26175258-5.902958223*I, ( 2 ) = 19.26175258+5.902958223*I, ( 3 ) = 6.932751694, ( 4 ) = 2.753709683, ( 5 ) = 1.451748259, ( 6 ) = .8907623630, ( 7 ) = .6006863100, ( 9 ) = .3252930815, ( 8 ) = .4319166022, ( 11 ) = .2033707803, ( 10 ) = .2537145109, ( 13 ) = .1390101296, ( 12 ) = .1666327589, ( 15 ) = .1009699238, ( 14 ) = .1177214819, ( 18 ) = 0.6764836348e-1, ( 19 ) = 0.6014940869e-1, ( 16 ) = 0.8755294957e-1, ( 17 ) = 0.7664134466e-1, ( 22 ) = 0.4385090431e-1, ( 23 ) = 0.3987062318e-1, ( 20 ) = 0.5383110866e-1, ( 21 ) = 0.4845811396e-1, ( 27 ) = 0.2835149444e-1, ( 26 ) = 0.3071130419e-1, ( 25 ) = 0.3337839456e-1, ( 24 ) = 0.3640850864e-1, ( 31 ) = 0.2118804423e-1, ( 30 ) = 0.2270014307e-1, ( 29 ) = 0.2438004471e-1, ( 28 ) = 0.2625352267e-1 ] )

  

19.26175258-5.902958223*I

  

6.932751694

 (1)
> 

 

Download oddProc2.mw

 

My $0.02...

tomleslie 13876
August 26 2022
0 1

is shown in the attached.

> 

  with(Student[Calculus1]):
  soln := remove
          ( `=`,
            I*~(Roots(y-0.4646295e-3*tanh(y)+0.1839145082e-2*tanh(y)/(0.6000000000e-3*y^2-0.1840000000e-2), y)),
            0
          );

[-.2381948477*I, -0.1434221912e-3*I, 0.1434221912e-3*I, .2381948477*I]

 (1)
> 

 

Download roots.mw

Use a sequence of strings...

tomleslie 13876
August 26 2022
1 1

as in the attached. Not sure why you have written the procedure Isee() - why not just use the Describe() command? Both methods are shown in the attached

> 

  restart;
  Isee:= proc(a)
             interface(verboseproc = 3);
             printf("%P", eval(a));
         end proc:
  Test:= proc(A,B,C)
         description "Computes projective line through 2 projective points or intersert",
                     "of 2 projective lines as a projective point or coincidence of point",
                     "line",
                     "Does some checking on validity of inputs.",
                     "Mobposn:- Global Variable, must = 1 or 3.",
                     "Points are returned as <1,x,y> or <x,y,1>",
                     "Lines are returned as <z,x,y> or <x,y,z>,",
                     "normalgpt :- Global Variable must be 0 or 1.",
                     "Points with algecraic elements are not reduced to <1,x,y> or <x,y,1> if 0",
                     "Points are defined as row vectors and  lines as column `vectors";
         print(A,B,A-C);

         end proc:
  Isee(Test);
  Describe(Test);

proc(A, B, C)
    description
    "Computes projective line through 2 projective points or intersert",
    "of 2 projective lines as a projective point or coincidence of point",
    "line", "Does some checking on validity of inputs.",
    "Mobposn:- Global Variable, must = 1 or 3.",
    "Points are returned as <1,x,y> or <x,y,1>",
    "Lines are returned as <z,x,y> or <x,y,z>,",
    "normalgpt :- Global Variable must be 0 or 1.", "Points with algecra\
    ic elements are not reduced to <1,x,y> or <x,y,1> if 0",
    "Points are defined as row vectors and  lines as column `vectors";
    print(A, B, A - C);
end proc
# Computes projective line through 2 projective points or intersert
# of 2 projective lines as a projective point or coincidence of point
# line
# Does some checking on validity of inputs.
# Mobposn:- Global Variable, must = 1 or 3.
# Points are returned as <1,x,y> or <x,y,1>
# Lines are returned as <z,x,y> or <x,y,z>,
# normalgpt :- Global Variable must be 0 or 1.
# Points with algecraic elements are not reduced to <1,x,y> or <x,y,1> if 0
# Points are defined as row vectors and lines as column `vectors
Test( A, B, C )
 

  
> 

 

Download desc.mw

Error message seems pretty clear...

tomleslie 13876
August 25 2022
0 3

ie

Error, (in rtable/Power) exponentiation operation not defined for Vectors

you can produce the power of a mxm matrix A, because A3=A.A.A and this multiplication is defined. However you cannot do this with a mx1 (or 1xm) vector V, because the underlying multipplication operation in V3=V.V.V is not defined. Try multiplying three vectors in the same orientation to see wht you get.

Maybe using vectors as the basic datatype in your calculation is a bad choice?

Trying to make further progress on this worksheet is difficult becalue there are so many undefined quantitties, but you may want to consider the (quick and dirty!) fixes in the attached, which at least evaluates to a couple of usable expressions

restart

``

``

This is a test file

``

NULL

NULL

N := 2.7

``

Hb := `<,>`(0.76e-1, 0.83e-1)

k := `<,>`(0.3400566801e-4, 0.3424620533e-4)

P50a := `<,>`(20.78938475, 21.39546041)

P50v := `<,>`(21.20711722, 22.06793197)

NULL

nu := `<,>`(0.2042461957e-1, 0.2120393111e-1)

Df := `<,>`(0.1617321837e-4, 0.1607066092e-4)

P__baro := `<,>`(759.062, 759.062)

Vector[column](%id = 36893488148090540988)

 (1)

PaCor := `<,>`(94.82734101, 90.40928915)

Vector[column](%id = 36893488148090534716)

 (2)

NULL

PvCor := `<,>`(35.32630403, 35.55779803)

Vector[column](%id = 36893488148090528940)

 (3)

f := [seq(1.34*N*Hb[ind]*(p/((P50a[ind]+P50v[ind])*(1/2)))^(N-1)/(((P50a[ind]+P50v[ind])*(1/2))*k[ind]*(1+(p/((P50a[ind]+P50v[ind])*(1/2)))^N)^2), ind = 1 .. 2)]

[2.176889645*p^1.7/(1+0.2692189148e-3*p^2.7)^2, 2.151698474*p^1.7/(1+0.2453845489e-3*p^2.7)^2]

 (4)

``

NULL

result := seq(Por*phi*(nu[j]/Df[j])^(2/3)*(Int((1+f[j])^(2/3)/(P__baro[j]-p), p = PvCor[j] .. PaCor[j]))/((4*(1-Por))*BP__length), j = 1 .. 2)
evalf(%)

10.73322003*Por*phi/((1.-1.*Por)*BP__length), 11.59819487*Por*phi/((1.-1.*Por)*BP__length)

 (5)

NULL

NULL

NULL

Download oddCalc.mw

 

The errors occur...

tomleslie 13876
August 25 2022
1 0

because neither the output from a texplot() or polygonplot() command is a geometric object whihc can be handled by the geometry:-draw() command.

The correct way to achieve what you want is to use the display() command, as in

plots:-display( [ geometry:-draw(whatever),
                         plots:-textplot(whatever)
                         plots:-polygonplot(whatever)
                      ]
                    )

As shown in the attached

> 

  restart:
  with(plots): with(geometry):
  _EnvHorizontalName := 'x':
  _EnvVerticalName := 'y':
  a := 7:
  point(E, 0, a*sqrt(3)/2):
  point(B, -a/2, 0):
  point(C, a/2, 0):
  point(o, 0, a*sqrt(3)/6):
  point(A, 0, a/2):
  point(H, 0, 0):
  R := (3-sqrt(3))*sqrt(2)*a/12:
  point(J, 0, a*sqrt(3)/6 - R):
  triangle(Tr1, [E, B, C]):
  triangle(Tr2, [A, B, C]):
  StretchRotation(E1, E, B, Pi/4, clockwise, sqrt(2)/2):
  coordinates(E1):
  StretchRotation(E2, E, C, Pi/4, counterclockwise, sqrt(2)/2):
  coordinates(E2):
  triangle(Tr3, [E, B, E1]):
  triangle(Tr4, [E, C, E2]):
  triangle(Tr5, [B, C, J]):
  circle(cir, [point(P1,[0,a*sqrt(3)/6]), R]):
  poly := Matrix( [ [0, a*sqrt(3)/2], [-7/4 + (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4],
                    [0, a/2],
                    [7/4 - (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4]
                  ],
                  datatype = float
                ):
  pol1 := polygonplot(poly, colour = "Magenta", transparency = 0.7, gridlines):
  tex := textplot([0.2, a*sqrt(3)/2, "zE"], 'align' = {'above', 'right'}):
  display( [ draw( [ Tr1(color = cyan),
                     Tr3(color = green),
                     cir(color=blue),
                     Tr2(color = red),
                     Tr4(color = grey),
                     Tr1(color=blue)],'view' = [-5 .. 5, 0 .. 7
                   ],
                   axes = normal,
                   scaling = constrained,
                   size=[800,800]
                   ),
            tex
           ]
          );

 
> 

  line(L1, [B, o]):
  Equation(L1):
  line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0):
  reflection(J1, J, L1):
  triangle(Tr6, [B, J1, E]):
  line(L2, [C, o]):
  Equation(L2):
  line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0):
  reflection(J3, J, L2):
  triangle(Tr7, [C, J3, E]):
  triangle(T1, [E, J1, A]):
  triangle(T2, [E, C, E2]):
  triangle(T3, [B, H, J]):
  triangle(T4, [C, H, J]):

  display( [ draw( [ cir(color = orange, filled = true, transparency = 0.1),
                     Tr6(color = blue, filled = true, transparency = 0.2),
                     Tr5(color = blue, filled = true, transparency = 0.2),
                     Tr7(color = blue, filled = true, transparency = 0.2),
                     T1(color = green, filled = true, transparency = 0.2),
                     T2(color = green, filled = true, transparency = 0.2),
                     T3(color = green, filled = true, transparency = 0.2),
                     T4(color = green, filled = true, transparency = 0.2)
                   ],
                   axes = none,
                   scaling = constrained
                 ),
             pol1
           ]
         );

                   

 
> 

 

Download geomDraw.mw

If I just work with the expression...

tomleslie 13876
August 25 2022
1 3

  expr:= x+I*y-0.4646295e-3*tan(x+I*y)+0.2758717622e-2*tan(x+I*y)/(0.6000000000e-3*(x+I*y)^2-0.2760000000e-2);

and assume that you want simultaneous solutions for Re(expr)=0, Im(expr)=0, then one obtains three possible answers. See the attached

> 

  restart;
  expr:=x+I*y-0.4646295e-3*tan(x+I*y)+0.2758717622e-2*tan(x+I*y)/(0.6000000000e-3*(x+I*y)^2-0.2760000000e-2):
#
# plot Re(expr)=0 and Im(expr)=0 - just to get
# some idea of where solutions might be
#
  plots:-implicitplot( [ Re(expr),Im(expr)],
                       x=-2..2,
                       y=-2..2,
                       color=[red,blue],
                       axes=boxed
                     );
#
# Hmmm solution (if any are very close to the origin
# so replot above with *much* smaller x,y ranges
#
  plots:-implicitplot( [ Re(expr),Im(expr)],
                         x=-0.0001..0.0001,
                         y=-0.0001..0.0001,
                         color=[red,blue],
                         axes=boxed
                       );
#
# Looks like there may be three solutions. From the above
# plot these are approximately
#
#          x= 0,       y=0
#          x=-0.00002, y=0
#          x= 0.00002, y=0
#
# Use fsolve with appropriate ranges to obtain these solutions
#
  f:=unapply( Re(expr), [x,y]):
  g:=unapply( Im(expr), [x,y]):
  fsolve( [f, g], [0..0.00005, -0.00005..0.00005]);
  fsolve( [f, g], [-0.00005..0, -0.00005..0.00005]);
  fsolve( [f, g], [-0.00001..0.00001, -0.00001..0.00001]);
 

 

 

[0.19535837429479822e-4, 0.]

  

[-0.19535837433966997e-4, 0.]

  

[0., 0.]

 (1)
> 

 

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