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| How to define a ring of differential operator https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2501 |
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| Author: | shox [ Mon Jul 06, 2015 9:56 pm ] |
| Post subject: | How to define a ring of differential operator |
Hello, i want to define and eventually construct a groebner basis for an Ideal in a Ring of differnetial operators, for example K[x1,.......xn][D1,.........,Dn] which should somehow be possible with nc_algebra (since the Ring is a g-algebra). Since i can only give singular information about variables i would can define how the xi and Dj interact with each other, but to compute a groebner basis, singular has to handle any element of K[x1,....,xn] as a coefficient . But x1x2 has to have the same degree as for example x1. I do not see a possibility how Singular will allow me to define the noncommutative properties of the ring and also handle any element out of K[x1,...,xn] the way it needs to (for example giving me x1+x2 as leading coefficient of (x1+x2)D1). Is there any possibility to solve my problem? best regards, kolja. |
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| Author: | hannes [ Thu Jul 09, 2015 10:22 am ] |
| Post subject: | Re: How to define a ring of differential operator |
Use a block ordering (as ordering for the variables x_i, Dx_i) which allows to consider the variables of the first Block as the main variables and the variables of the second block as "coeffcients". See Gianni, P.; Trager, B.;Zacharias, G.: Gröbner bases and Primary Decomposition of Polynomial Ideals. Journal of Symbolic Computation. 1985. for details, here this trick is used to compute Groebner basesin K[x_i][y_i] but it works also in the non-commutative case. |
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| Author: | Guest [ Thu Jul 09, 2015 5:52 pm ] |
| Post subject: | Re: How to define a ring of differential operator |
Thank you very much, i will try that |
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| Author: | levandov [ Wed Sep 30, 2015 4:28 pm ] |
| Post subject: | Re: How to define a ring of differential operator |
the library ratgb.lib does this automatically and in a user-friendly way. see e.g. http://www.singular.uni-kl.de/Manual/4-0-2/sing_813.htm |
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