Timeline for How to define a non-standard algebra in Mathematica?
Current License: CC BY-SA 3.0
13 events
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| May 21, 2012 at 14:30 | comment | added | celtschk |
@Anixx: Commutativity should already be accounted for by the line SetAttributes[#,Orderless]&/@{plus,times};. To account for associativity as well, you can change Orderless to {Flat,Orderless} in that line. I don't think there's an attribute for distributivity, though.
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| May 21, 2012 at 5:58 | comment | added | Anixx | But can it automatically simplify the expressions with unknown variables? For example, simplify $(a\otimes b)\oplus (a\otimes c)$ to $a\otimes (b\oplus c)$? | |
| May 21, 2012 at 5:53 | vote | accept | Anixx | ||
| May 21, 2012 at 2:49 | comment | added | J. M.'s missing motivation♦ |
Also, Function[{a, b, c}, a\[CircleTimes](b\[CirclePlus]c) == (a\[CircleTimes]b)\[CirclePlus](a\[CircleTimes]c)] @@@ Apply[Join, Permutations /@ Tuples[{0, 1, Infinity}, 3]]
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| May 21, 2012 at 2:47 | comment | added | J. M.'s missing motivation♦ |
@Anixx: okay then... Function[{a, b, c}, a\[CirclePlus](b\[CirclePlus]c) == (a\[CirclePlus]b)\[CirclePlus]c] @@@ Apply[Join, Permutations /@ Tuples[{0, 1, Infinity}, 3]]
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| May 21, 2012 at 2:43 | comment | added | Anixx | I want it do derive all the properties of the new algebra for itself, just taking the tables of addition and multiplication as the input. | |
| May 21, 2012 at 2:42 | comment | added | Anixx | the tables I provided are enough for such derivation. | |
| May 21, 2012 at 2:41 | comment | added | Anixx | I wonder whether it will derive associativity ans distributivity laws itself. | |
| May 21, 2012 at 2:39 | comment | added | J. M.'s missing motivation♦ | @Anixx: why not try it out yourself? BTW: you didn't mention if associativity is a property of your algebra... | |
| May 21, 2012 at 2:38 | comment | added | rm -rf♦ | what sort of expressions do you have in mind? Have you tried it with your expressions? You should add such info to the question before posting. | |
| May 21, 2012 at 2:37 | history | edited | rm -rf♦ | CC BY-SA 3.0 |
added 155 characters in body
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| May 21, 2012 at 2:37 | comment | added | Anixx | Will it simplify complex expressions? | |
| May 21, 2012 at 2:31 | history | answered | rm -rf♦ | CC BY-SA 3.0 |