MaplePrimes - answers and comments on Question, Strange subs problem

Re

Kitonum — Wed, 23 Jan 2013 09:45:48 Z

f:= A^2-2*sqrt(A^2+1)+1;

f2:= simplify(algsubs(A^2+1 = M^2, f)) assuming M>0;

f := A^2-2*(A^2+1)^(1/2)+1

f2 := M^2-2*M

Another way

Markiyan Hirnyk — Wed, 23 Jan 2013 09:56:54 Z

> assume(A > 0); interface(showassumed = 0); f := A^2-2*sqrt(A^2+1)+1:
> eval(f, [A^2+1 = M, A^2 = M-1]);

M - 2* M ^(1/2)

It should be noticed that M is not assumed (see assume.mw ). In case of need, it is made additionally

assume(M>1);
Also try "subs" , "algsubs", and "eval" search in MaplePrimes at the top of this page because similar questions were asked and answered many times.

PS. This change can also be produced by the Menu/Edit/ Find/Replace button in Maple worksheet.

PPS. See ?subs , ?algsubs , and ?eval for mor details.

Use algsubs rather than subs

Carl Love — Wed, 23 Jan 2013 10:24:54 Z

The subs command only does "syntactic" substitutions, i.e. the item being substitued for must occur as a distinct entity within Maple's internal representation of the expression. It is more of a "programmer level" command than "user level", and it makes no claim as to the mathematical validity of what it does. To perform algebraically valid substitutions, use algsubs.

subs for A^2

roman_pearce — Thu, 24 Jan 2013 17:22:57 Z

subs can't isolate A^2+1 in the outermost level. A quick fix is to substitute for A^2.

f:= A^2-2*sqrt(A^2+1)+1;

subs(A^2=M^2-1, f);

Then you may want to simplify it, etc.

Side relation

Adri van der Meer — Fri, 25 Jan 2013 19:07:57 Z

simplify( f, {A^2+1=M^2} ) assuming M>0;
                              (1/2)     
                          / 2\         2
                       -2 \M /      + M

Strange, that another simplification is needed for sqrt(M^2):

simplify( simplify( f, {A^2+1=M^2} ) ) assuming M>0;
                                   2
                           -2 M + M

Simplification

Markiyan Hirnyk — Wed, 23 Jan 2013 10:21:13 Z

It also works without the simplify command in Maple 16.02

> restart; f := A^2-2*sqrt(A^2+1)+1: f2 := `assuming`([algsubs(A^2+1 = M^2, f)], [M > 0]);

> M;

but the assumption is not produced (This code should be executed on a new worksheet with a new engine.).