#### Assume problem (15.4.97)

##### Jaroslav Hajtmar

I am a beginner to Maple V rel. 4 and a novice on Maple User Group. I have two ”assume” questions.

1) I think, that "assume(...)" command has no inﬂuence on solving equations. Is it true?

for example :

Why does Maple compute real roots? Assume(x,real) has no eﬀect ? Or where is the mistake?

2) I want to use ”assume” command for variable x from RealRange(-infinity, Open(-2)) or from RealRange(Open(2), infinity) (union intervals)

Is it possible?

##### Robert Israel(21.4.97)

| 1) I think, that "assume(...)" command has no influence on ...

It doesn’t restrict the values that ”solve” will ﬁnd. I wouldn’t quite say it ”has no inﬂuence”, because it may in fact inﬂuence transformations of the equations that occur in the process of solving them. For example:

This is because sqrt(x^2) is simpliﬁed to x while sqrt(y^2) is simpliﬁed to -y (actually, before ”solve” even starts).

| Why does Maple compute real roots? Assume(x,real) has no effect ?

It doesn’t cause Maple to check whether the results satisfy the assumptions.

Actually, Maple doesn’t even know whether or not sqrt(-4+m^2) is real.

although it does know that -4+m^2 < 0:

But even if it did know, it wouldn’t restrict the values obtained for x.

You can sometimes restrict the output of ”solve” by including inequalities. For example:

However, this usually doesn’t work if there are symbolic parameters.

(No result is returned)

And, strangely enough (still with the same assumption on m):

(Note to Maple developers: this is a bug)

(No result in Maple V Release 5, U. Klein)

| 2) I want to use "assume" command for variable x from ...

Yes.

##### Willard, Daniel (DUSA) (23.4.97)

Be aware that ”assume” carries no weight with ”type”. In BesselI(x,y), for example, the Maple routine requires y to be of type integer, and preceding its use with the command "assume(y,integer)" does not get past the typing check early in the program.

Stupid!. I have complained to Maple about it without any observable improvement.

##### Robert Israel (24.4.97)

| Be aware that "assume" carries no weight with "type". ...