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sursumCorda

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Why do I have to evaluate the outer `Roo...

sursumCorda 1284 Maple 2024
rootof
September 17 2024
1 4

The first time they are evaluated, some aborts can occur; the second time they are evaluated, no exception is thrown: 
 

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1806 and is the same as the version installed in this computer, created 2024, September 11, 11:27 hours Pacific Time.`

 (1)
> 

restart;
> 

RootOf(
        9*x1-5+RootOf(8*_Z**2+_Z-43, 41629632769253767815/18446744073709551616 .. 20814816384626883921/9223372036854775808), x1, 171590466306199/562949953421312 .. 343180932612401/1125899906842624
);

Error, (in property/ProbablyNonZero) cannot determine if this expression is true or false: ln(.1e11*abs(-.304805898398896+1.*RealRange(.304805898398895,.304805898398897)))/ln(10) < -6

  
> 

RootOf(
        9*x1-5+RootOf(8*_Z**2+_Z-43, 41629632769253767815/18446744073709551616 .. 20814816384626883921/9223372036854775808), x1, 171590466306199/562949953421312 .. 343180932612401/1125899906842624
);

5/9-(1/9)*RootOf(8*_Z^2+_Z-43, 41629632769253767815/18446744073709551616 .. 20814816384626883921/9223372036854775808)

 (2)
> 

RootOf(
        2*x1-3+RootOf(_Z**2+2*_Z-11, 181818607464242035159/73786976294838206464 .. 363637214928484070345/147573952589676412928), x1, 301683970796757/1125899906842624 .. 150841985398379/562949953421312
);

Error, (in property/ProbablyNonZero) cannot determine if this expression is true or false: ln(2500000000.*abs(-.267949192431123+1.*RealRange(.267949192431122,.267949192431123)))/ln(10) < -6

  
> 

RootOf(
        2*x1-3+RootOf(_Z**2+2*_Z-11, 181818607464242035159/73786976294838206464 .. 363637214928484070345/147573952589676412928), x1, 301683970796757/1125899906842624 .. 150841985398379/562949953421312
);

3/2-(1/2)*RootOf(_Z^2+2*_Z-11, 181818607464242035159/73786976294838206464 .. 363637214928484070345/147573952589676412928)

 (3)


 

Download run__twice.mw

Why does (the outer) RootOf have to be evaluated twice? 
Note. There are other similar examples, but they are less concise (so they are omitted here).

could be or could not be...

sursumCorda 1284 Maple 2024
realdomain coulditbe smtlib
September 16 2024
2 9

I have a quite complex expression (where and are real numbers): 

expr := Or(And(-p^2 + 3*q < 0, p < 0, p^2 - 4*q < 0, Or(And(p < 0, -q < 0), p < 0, q < 0), Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0))), Or(And(Or(And(p < 0, -q < 0), p < 0, q < 0), Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0)))), And(p < 0, -q < 0), p < 0, q < 0, And(2*p^2 - 3*q < 0, -q^2 < 0), And(-p <= 0, Or(2*p^2 - 3*q < 0, q^2 < 0))), -2*p^5 + 15*p^3*q - 27*p*q^2 <= 0, p^2*q^2 - 4*q^3 = 0), And(p^2 - 3*q = 0, p < 0, -2*p^2 + 3*q < 0, Or(And(p < 0, -2*p^2 + 3*q < 0), p < 0, 2*p^2 - 3*q < 0), 2*p^3 - 9*p*q = 0), And(-p^2 + 3*q < 0, Or(And(p < 0, p^2 - 4*q < 0), p < 0, -p^2 + 4*q < 0), p < 0, -q < 0, Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(-p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0))), Or(And(p < 0, -q < 0, Or(And(-2*p^2 + 3*q < 0, -q^2 < 0), And(-p <= 0, Or(-2*p^2 + 3*q < 0, q^2 < 0)))), And(p < 0, -q < 0), And(2*p^2 - 3*q < 0, -q^2 < 0), And(p <= 0, Or(2*p^2 - 3*q < 0, q^2 < 0))), 2*p^5 - 15*p^3*q + 27*p*q^2 <= 0, p^2*q^2 - 4*q^3 = 0)):

According to coulditbe, is satisfiable: 

_EnvTry := 'hard':
coulditbe(expr) assuming real;
 = 
                              true

But according to SMTLIB:-Satisfiable, is not satisfiable: 

SMTLIB:-Satisfiable(expr) assuming real;
 = 
                             false

Why are the two results opposite? 

For reference, below is the output from RealDomain:-solve: 

RealDomain:-solve(expr);
 = 
               /           1  2\                 
              { p = p, q = - p  }, {p = p, q = 0}
               \           4   /

I also tried using RealDomain:-simplify, yet the output remains almost unchanged (Why?). 

Reproduce a well-known result? ...

sursumCorda 1284 Maple 2024
polynomial solve rootof
September 14 2024
1 3

A classic result states that the equation x3＋px2＋qx＋r＝0 with real coefficients p, q, r has positive roots iff p＜0, q＞0, r＜0 and -27r2 - 2p(2p2 - 9q)r + q2(p2 - 4q) ⩾ 0 (see for example this question). 
However, Maple appears unable to find the condition: 

a, b, c := allvalues(RootOf(x^3 + p*x^2 + q*x + r, x), 'implicit'):
RealDomain:-solve({a, b, c} >~ 0, [p, q, r]);
 = 
Warning, solutions may have been lost
                               []

Is there a way to get the above conditions in Maple with as little human intervention as possible (I mean, without a priori knowledge of the theory of polynomials)? 

Edit. An interesting problem is when these three positive roots can further be the lengths of sides of a triangle. For reference, here are some (unenlightening) results from some other software: 

interface('longdelim' = false): doesn't ...

sursumCorda 1284 Maple 2024
September 10 2024
1 4

The help page of interface('longdelim') states: 

If true, Maple control structures such as if, do, proc, and so on are displayed with the newer-style long ending delimiters such as end if, end do, end proc, and so on. If false, ending delimiters are displayed as fi, od, end, and so on. 

If I set interface('longdelim' = false):, the Maple Input

try f:=0 catch:end try;

can be converted into 

via , but why is

use f=0 in f+1 end use;

still converted into

 instead of “use f = 0 in f + 1 end”? 

What is the usage of seq(depends(type))?...

sursumCorda 1284 Maple
parameters procedure argument
September 10 2024
1 1

According to the documentation, 

the depends modifier can be used in declaration to indicate that a parameter's type depends on the value of another parameter, the seq modifier declares that multiple arguments of a specific type within a procedure invocation will be assigned to a single parameter, and if the depends modifier is used together with the seq modifier, the declaration must be written: . 

So the code below works as expected: 

f0 := proc(x::Not(2), y::2) [[x], [y]] end:
f0(1, 2);
                           [[1], [2]]

f0(2, 2);
Error, invalid input: f0 expects its 1st argument, x, to be of type Not(2), but received 2

The code below also works as expected: 

f1 := proc(x::depends(Not(y)), y::2) [[x], [y]] end:
f1(1, 2);
                           [[1], [2]]

f1(2, 2);
Error, invalid input: f1 expects its 1st argument, x, to be of type Not(2), but received 2

The code below works as desired as well: 

f2 := proc(x::seq(Not(2)), y::2) [[x], [y]] end:
f2(0, 1, 2);
                         [[0, 1], [2]]

f2(2, 1, 2);
                           [[], [2]]

However, the following code does not work: 

f3 := proc(x::seq(depends(Not(y))), y::2) [[x], [y]] end:
f3(0, 1, 2);
Error, invalid input: NULL uses a 2nd argument, y (of type 2), which is missing
f3(2, 1, 2);
Error, invalid input: NULL uses a 2nd argument, y (of type 2), which is missing

I believe that the output of  and  should be the same as that of  and  respectively. Did I miss something? 

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