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Honigmelone

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@radaar  thanks for your answer. E...

Honigmelone 102
February 06 2020
0 0

@radaar 

thanks for your answer. Even though the optimisation works this way, g(x) is not inlcuded in the function to optimze.

@acer  Thanks for the exhaustive a...

Honigmelone 102
February 06 2020
0 0

@acer 

Thanks for the exhaustive answer! This has solved the question.

@Carl Love  I don't have a str...

Honigmelone 102
February 06 2020
0 0

@Carl Love 

I don't have a strict 1D input here, but wanted to focus on the 1D problem first.

Nevertheless I should have excluded these additionall points from the question.

@acer I can't quite recall why I us...

Honigmelone 102
July 30 2018
0 0

@acer

I can't quite recall why I used eval(alist,1), but for me the problem persists when I dont use it, or even redifine the list as clist. I fiddeled a bit more, and the only way to get rid of the assumptions seems to be to manually redefine everything.

In the following code snipped I define funa, funb, and func as well as alist, blist and clist before and after making assumptions on x and y, as well as after removing them again:

> 

 

> 

restart:
> 

 

> 

# test removing assumptions
> 

# define first function before assuming
> 

funa:=x+y

x+y

 (1)
> 

 Maple_proc := codegen[makeproc](funa,(ListTools[Flatten]([eval(alist,1)])));

proc (alist) x+y end proc

 (2)
> 

#place variables in a list
> 

alist:=[x,y];

[x, y]

 (3)
> 

 

> 

# make some assumptions
> 

assume(x,real);assume(y,real);
> 

x,y

x, y

 (4)
> 

#place variables in a list
> 

blist:=[x,y];

[x, y]

 (5)
> 

# define second function after assuming
> 

funb := x+y;

x+y

 (6)
> 

 

> 

# make cool interferences with assumptions...
> 

# clear assumptions

> 

# try 1 from https://www.mapleprimes.com/questions/207601-Remove-Assumptions-
> 

nms:=convert(indets(alist,name),list);
nmsS:=convert~(nms,string);
L:=StringTools:-Substitute~(nmsS,"~",""); #Removing "~"
L1:=parse~(L);
S:=nms=~L1;
Expr:=subs(S,expr);

[x, y]

  

["x~", "y~"]

  

["x", "y"]

  

[x, y]

  

[x = x, y = y]

  

expr

 (7)
> 

hasassumptions(x)

true

 (8)
> 

# try 2

> 

nops(alist)

2

 (9)
> 

for i from 1 to nops(alist) do
parse(cat(StringTools[Substitute]~(alist[i],"~",""),":='",StringTools[Substitute]~(alist[i],"~",""),"'"));
end do;

'x'

  

'y'

 (10)
> 

# check if assumtions are there
> 

hasassumptions(x)

true

 (11)
> 

#try 3 https://www.mapleprimes.com/questions/39555-Unassume
> 

for u in alist do
`property/object`[u]:=evaln(`property/object`[u]);
`property/OrigName`[u]:=evaln(`property/OrigName`[u]);
end do;

`property/object`[x]

  

`property/OrigName`[x]

  

`property/object`[y]

  

`property/OrigName`[y]

 (12)
> 

hasassumptions(x)

false

 (13)
> 

hasassumptions(y)

false

 (14)
> 

alist;blist;

[x, y]

  

[x, y]

 (15)
> 

hasassumptions(eval(alist,1));hasassumptions(eval(blist,1))

false

  

false

 (16)
> 

hasassumptions(alist);hasassumptions(blist);

false

  

false

 (17)
> 

hasassumptions(funa);hasassumptions(funb);

false

  

false

 (18)
> 

# define third function after automated removal of assumptions
> 

func:=x+y

x+y

 (19)
> 

clist:=[x,y]

[x, y]

 (20)
> 

hasassumptions(func);hasassumptions(clist);

false

  

false

 (21)
> 

# test if assumtions are present after usage of makeproc
> 

 Maple_proc := codegen[makeproc](funa,(ListTools[Flatten]([alist]))); #fail

proc (x, y) x+y end proc

 (22)
> 

 Maple_proc := codegen[makeproc](funb,(ListTools[Flatten]([blist]))); #fail

proc (x, y) x+y end proc

 (23)
> 

 Maple_proc := codegen[makeproc](func,(ListTools[Flatten]([clist]))); #fail

proc (x, y) x+y end proc

 (24)
> 

 Maple_proc := codegen[makeproc](funa,([x,y])); #fail

proc (x, y) x+y end proc

 (25)
> 

# try 4
> 

# manual unevaluation of x and y
> 

x:='x';y:='y'

x

  

y

 (26)
> 

# define list and function
> 

fund := x+y

x+y

 (27)
> 

dlist:=[x,y]

[x, y]

 (28)
> 

 Maple_proc := codegen[makeproc](funa,(ListTools[Flatten]([alist]))); #succes

proc (x, y) x+y end proc

 (29)
> 

 Maple_proc := codegen[makeproc](funb,(ListTools[Flatten]([blist]))); #fail

proc (x, y) x+y end proc

 (30)
> 

 Maple_proc := codegen[makeproc](func,(ListTools[Flatten]([clist]))); #fail

proc (x, y) x+y end proc

 (31)
> 

 Maple_proc := codegen[makeproc](fund,dlist); #success

proc (x, y) x+y end proc

 (32)
> 

 

> 

 

> 

 


 

Download testunassuming.mw

@John May Thanks, removing the ticks aro...

Honigmelone 102
May 31 2017
0 0

@John May Thanks, removing the ticks around the expand did the trick.

Thanks!...

Honigmelone 102
September 14 2016
0 0

@Markiyan Hirnyk @also

Thanks very much! That worked for me. Since I don't really understand what numeric does, I will flag the fist reply as answer.

found the problem...

Honigmelone 102
April 14 2016
0 0

@tomleslie 

hey tomleslie,

thanks for looking into the issue. The problem was indeed in my long script. It happes that I use a variable called "a" there. When this variable is loaded before any rule using the name "a" is echoed or applied behavior becomes strange. See the attached script for reference:


> 

restart;
> 

rule:=abs(''a''::algebraic)^2=''a''^2;

abs('a'::algebraic)^2 = 'a'^2

 (1)
> 

someotherrule:=abs(''w''::algebraic)^2=''w''^2;

abs('w'::algebraic)^2 = 'w'^2

 (2)
> 

# applyrule(rule,abs(x)^2); #uncommenting ether of these will solve the problem
> 

# rule;
> 

applyrule(someotherrule,abs(x)^2); #applying a rule without "a" has no influence

x^2

 (3)
> 

a:=1; #a loaded before echoing rule

1

 (4)
> 

rule:=abs(''a''::algebraic)^2=''a''^2;

abs('a'::algebraic)^2 = 'a'^2

 (5)
> 

rule; #strange behavior

a::algebraic^2 = a^2

 (6)
> 

applyrule(rule,abs(x)^2); #cannot work as rule is diffrent from what has been defined.

abs(x)^2

 (7)
> 

 


Download applyrule_3.mw

thanks!...

Honigmelone 102
April 12 2016
0 1

@Preben Alsholm 

Thanks, that was what I was looking for!

Thanks...

Honigmelone 102
April 12 2016
0 0

@Preben Alsholm 

Thanks, I will try that!

even better...

Honigmelone 102
March 04 2016
0 0

@acer 

thanks, I appreciate all improvement suggestions for clean code:)

Follow up, assign in tables and vectors...

Honigmelone 102
March 04 2016
0 0

@Kitonum 

Just for the record: I found that even though assign also works with tables, it only works there once:


> 

restart;
> 

av:=<av1,av2,av3>;

av := Vector(3, {(1) = av1, (2) = av2, (3) = av3})

 (1)
> 

assign(av(1),3);
> 

assign(av(1),5);

> 

av1;                          #works with vectors

5

 (2)
> 

atv:=table([atv1,atv2,atv3]);

table( [( 1 ) = atv1, ( 2 ) = atv2, ( 3 ) = atv3 ] )

 (3)
> 

atvv:=convert(convert(atv,list),Vector);

atvv := Vector(3, {(1) = atv1, (2) = atv2, (3) = atv3})

 (4)
> 

assign(atvv(1),3);
> 

assign(atvv(1),5);    
> 

atv[1];                          #works when converting the table to vector before assigning

5

 (5)
> 

at:=table([at1,at2,at3]);

table( [( 1 ) = at1, ( 2 ) = at2, ( 3 ) = at3 ] )

 (6)
> 

assign(at[1],3);
> 

assign(at[1],5);

Error, invalid left hand side in assignment

  
> 

at[1];      #expected result: 5

3

 (7)
> 

 


Download assign_table.mw

 

A workaround to this is to convert the table to a vector for assigning values to the tables variables. My guess is that the tables become updated when assigning, so that the link to its variable is lost.

Thanks!...

Honigmelone 102
March 04 2016
0 2

@Christian Wolinski 

Hey,

thank you for your second answer. To be honest I don't really understand how this function works, I am still very new at maple. But it does what it shall do. I love how you assume inside your funtion, but don't carry your assumptions to the output. That will definitely be useful later on.

However, please understand that I marked Carl Loves post as answer to this question, because his solution is a bit easier to understand.

Thanks again!...

Honigmelone 102
March 04 2016
0 1

@Carl Love 

Hey, thanks again! I would have never guessed to use a second rule. Now it works like a charm and does exactly what I wanted it to do. In order to be able to use the rule on Vectors I had to convert a bit:


> 

restart:
> 

f_symbol:=<abs(a-b)*abs(1,a-b),abs(b-c)*abs(1,b-c)>:  
> 

rule:= abs(''a''::algebraic)*abs(1,''a''::algebraic)= ''a'':
> 

rule2:= abs('expand'(-''a'')::algebraic)*abs(1, ''a''::algebraic)= ''a'':
> 

applyrule([rule,rule2],f_symbol); #expected result: a(t)-b

Vector(2, {(1) = abs(a-b)*abs(1, a-b), (2) = abs(b-c)*abs(1, b-c)})

 (1)
> 

convert(applyrule([rule,rule2],convert(f_symbol,list)),Vector);

Vector(2, {(1) = a-b, (2) = b-c})

 (2)
> 

 

> 

 


Download simplify_abs.mw

Thanks, how to apply to terms with funct...

Honigmelone 102
March 03 2016
0 0

@Carl Love 

Hey,

thanks, that is exactly what I asked for. However I want to apply this to an expression with functions in it. I don't really understand why it does not work, as a(t)-b is also algebraic. I already tried freeze with no success:

> 

restart:
> 

f_symbol:=abs(a-b)*abs(1,a-b):  
> 

f_fun:=abs(a(t)-b)*abs(1,a(t)-b);

abs(-a(t)+b)*abs(1, a(t)-b)

 (1)
> 

f_subs:=subs(a(t)=freeze(a(t)),f_fun);

abs(-`freeze/R0`+b)*abs(1, `freeze/R0`-b)

 (2)
> 

rule:= abs(''a''::algebraic)*abs(1,''a''::algebraic)= ''a'':
> 

applyrule(rule,f_fun); #expected result: a(t)-b

abs(-a(t)+b)*abs(1, a(t)-b)

 (3)
> 

applyrule(rule,f_subs);

abs(-`freeze/R0`+b)*abs(1, `freeze/R0`-b)

 (4)
> 

thaw(%);               #expected result: a(t)-b

abs(-a(t)+b)*abs(1, a(t)-b)

 (5)
> 

applyrule(rule,f_symbol);        #works

a-b

 (6)
> 

type(''a(t)-b'',algebraic);

true

 (7)
> 

 

> 

 


Download simplify_abs.mw

 

thanks...

Honigmelone 102
March 03 2016
0 3

@Thomas Richard 

hey, thanks for your solution! The warning to the symbolic options is pretty scary, but since I only have real variables and functions I don't have to worry.

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