Re: [Axiom-mail] A little simplification problem
Why? I didn't write the code but my best guess is that such rules would slow things down dramatically if they had to be applied everytime there's a + or - or * in Expression. You could experiment with your own Expression domain, adding more simplification rules and attaching them to the basic arithmetic ops. The current Expression implementation relies on the use of normalize for when you want to eliminate algebraically redundant kernels (informally, subexpressions). There's still the question of why does simplify not call normalize. I don't know the answer. Themos Tsikas On Saturday 02 August 2008, Alasdair McAndrew wrote: Thank you! In fact the rule expandPowers := rule x^(n+k) == x*x^(n+k-1) also seems to work well. But why does Axiom not automatically apply this rule for simplification of expressions involving powers, as other CAS's (Maple, Maxima, Mathematica) do? Thanks again, Alasdair On Sat, Aug 2, 2008 at 12:41 AM, Themos Tsikas [EMAIL PROTECTED] wrote: On Friday 01 August 2008, Alasdair McAndrew wrote: f(n)==7^n f(n+1)-7*f(n) simplify(%) normalize % The Numerical Algorithms Group Ltd is a company registered in England and Wales with company number 1249803. The registered office is: Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, United Kingdom. This e-mail has been scanned for all viruses by Star. The service is powered by MessageLabs. ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
[Axiom-mail] A little simplification problem
f(n)==7^n f(n+1)-7*f(n) simplify(%) What do I need to do to enable the final statement to produce 0? Thanks, Alasdair -- Blog: http://amca01.wordpress.com ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] A little simplification problem
On 08/01/2008 04:18 PM, Alasdair McAndrew wrote: f(n)==7^n f(n+1)-7*f(n) simplify(%) What do I need to do to enable the final statement to produce 0? Does that help? (1) - f(n)==7^n Type: Void (2) - a := f(n+1)-f(n)*7 n + 1 n (2) 7 - 7 7 Type: Expression Integer (3) - r := rule x^(y+1)==x*x^y y + 1 y (3) x == x x Type: RewriteRule(Integer,Integer,Expression Integer) (4) - r a (4) 0 Type: Expression Integer ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] A little simplification problem
On Fri, Aug 1, 2008 at 10:18 AM, Alasdair McAndrew wrote: f(n)==7^n f(n+1)-7*f(n) simplify(%) What do I need to do to enable the final statement to produce 0? You might use a pattern like this: (1) - f(n)==7^n Type: Void (2) - f(n+1)-7*f(n) n + 1 n (2) 7 - 7 7 Type: Expression Integer (3) - expandPowers := rule x^(n+1) == x*x^n n + 1 n (3) x == x x Type: RewriteRule(Integer,Integer,Expression Integer) (4) - expandPowers( %% 2) (4) 0 Type: Expression Integer - Regards, Bill Page. ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] A little simplification problem
Thank you! In fact the rule expandPowers := rule x^(n+k) == x*x^(n+k-1) also seems to work well. But why does Axiom not automatically apply this rule for simplification of expressions involving powers, as other CAS's (Maple, Maxima, Mathematica) do? Thanks again, Alasdair On Sat, Aug 2, 2008 at 12:41 AM, Themos Tsikas [EMAIL PROTECTED] wrote: On Friday 01 August 2008, Alasdair McAndrew wrote: f(n)==7^n f(n+1)-7*f(n) simplify(%) normalize % The Numerical Algorithms Group Ltd is a company registered in England and Wales with company number 1249803. The registered office is: Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, United Kingdom. This e-mail has been scanned for all viruses by Star. The service is powered by MessageLabs. ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail -- Blog: http://amca01.wordpress.com ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
Re: [Axiom-mail] A little simplification problem
expandPowers := rule x^(n+k) == x*x^(n+k-1) also seems to work well. But why does Axiom not automatically apply this rule for simplification of expressions involving powers, as other CAS's (Maple, Maxima, Mathematica) do? Maybe some people like to apply it in the other direction... contractPowers := rule x*x^n == x^(n+1) or even combinePowers := rule x^a*x^b == x^(a+b) Have you ever tried to apply the above rule as follows? expandPowers(x^(n+k)) Be sure to be close to Ctrl-C, since that seems to run forever. Ralf ___ Axiom-mail mailing list Axiom-mail@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-mail
