#608 taylor(x^a,[x],0,1) unsimplified

[Stavros Macrakis]

taylor(x^a,[x],0,1) => 1^2*x^a+...

Note unsimplified 1^2.

[Barton Willis]

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Maybe there is a connection between this
bug and bug 974734.

Barton

[Kris Katterjohn]

Here are some other simple examples:

(%i1) taylor(x^a,[x],0,1);
(%o1) +1^2*x^a

(%i2) taylor((x*y)^a,[x,y],0,1);
(%o2) +1^4*(x*y)^a

(%i3) taylor(x^a+y^a,[x,y],0,1);
(%o3) +(1^2*y^a+1^2*x^a)

(So, it's easy to get 1 raised to a large exponent and to get a bunch of unsimplified factors of 1 raised to stuff in multiple terms.)

In SETUP-MULTIVAR-DISREP genvars associated with multivars are set up with a DISREP property so they disrep to 1.

Up until a couple of weeks ago when I fixed bugs [#1848]/[#2446], you could see these internal gensyms that disrep to 1 by using taytorat:

(%i4) taylor(x^a,[x],0,1);
(%o4) +1^2*x^a

(%i5) taytorat(%); /* commit 38d4b2 fixed gensym leak */
(%o5) (g536^a)^2*x^a

Anyway, these visible unsimplified factors like 1^2 are introduced during disrep in PDISREP!. This function contains some special knowledge such as foo^0 is equal to 1 and foo^1 is equal to foo. We can add to PDISREP! the knowledge that 1^bar is equal to 1:

diff --git a/src/rat3e.lisp b/src/rat3e.lisp
index 99a8eb594..6ede4611c 100644
--- a/src/rat3e.lisp
+++ b/src/rat3e.lisp
@@ -924,6 +924,7 @@
                                 (eq (caar var) 'mplus))
                             (copy-list var))
                            (t var)))

+       ((eql var 1) 1)
        (t (list '(mexpt ratsimp) var n))))

 (defun pdisrep+ (p)

This causes no problems with the test suite or share test suite. And then we have this:

(%i8) taylor(x^a,[x],0,1);
(%o8) +x^a

(%i9) taylor((x*y)^a,[x,y],0,1);
(%o9) +(x*y)^a

(%i10) taylor(x^a+y^a,[x,y],0,1);
(%o10) +(y^a+x^a)

[Kris Katterjohn]

My patch does not fix bug [#577], which Barton had suspected might be related. That seems to be a separate bug.

[Kris Katterjohn]

Fixed by commit [f1ccc6].