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Re: [Axiom-developer] Examples for good types
From: |
Martin Rubey |
Subject: |
Re: [Axiom-developer] Examples for good types |
Date: |
28 Mar 2007 10:45:53 +0200 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |
Dear all,
Please reply only to axiom-math.
I very recently discovered another example, which I find (personally) more
convincing.
Axiom has a (rather weak, but still) domain for symmetric functions.
The multiplication of two symmetric functions goes as follows:
(7) -> powerSum 4 * powerSum 2 * powerSum 2 * powerSum 2
3
(7) (4 2 )
Type: SymmetricPolynomial Fraction Integer
(i.e., it is represented as an integer partition, where equal parts are, as
customary, written as exponents.)
Symmetric Functions like determinants a lot, especially in Axiom:
m := matrix [[complete 1, complete 0],[complete 2, complete 1]]
+ (1) [] +
| |
(2) |1 1 2 |
|- (2) + - (1 ) (1)|
+2 2 +
Type: Matrix SymmetricPolynomial Fraction Integer
(3) -> determinant m
1 1 2
(3) - - (2) + - (1 )
2 2
Type: SymmetricPolynomial Fraction Integer
Note that Axiom uses the product in the ring of symmetric functions to compute
the determinant. To check, by Jacobi-Trudi the result should coincide with the
Schur function corresponding to the partition $(1,1)$:
(4) -> SFunction [1,1]
1 1 2
(4) - - (2) + - (1 )
2 2
Type: SymmetricPolynomial Fraction Integer
Martin
- [Axiom-developer] CAS for the masses, daly, 2007/03/28
- Re: [Axiom-developer] CAS for the masses, Gabriel Dos Reis, 2007/03/28
- Re: [Axiom-developer] CAS for the masses, Ondrej Certik, 2007/03/28
- Re: [Axiom-developer] CAS for the masses, Ralf Hemmecke, 2007/03/28
- [Axiom-developer] Re: Advantage of Types and different representations, Martin Rubey, 2007/03/28
- Re: [Axiom-developer] CAS for the masses, Gabriel Dos Reis, 2007/03/28
- Re: [Axiom-developer] CAS for the masses, Ondrej Certik, 2007/03/28
- RE: [Axiom-developer] CAS for the masses, Bill Page, 2007/03/29
- Re: [Axiom-developer] CAS for the masses, Ondrej Certik, 2007/03/29
- RE: [Axiom-developer] CAS for the masses, Bill Page, 2007/03/29
- Re: [Axiom-developer] CAS for the masses, Ralf Hemmecke, 2007/03/29