Sorry I meant :: answer b. "return the maximum of the degrees of the homogeneous summands"
> I think that the default behaviour for categories like GradedAlgebra, GradedAlgebraWithBasis, GradedModule, ... should be to return an error if the element is not homogeneous. I have some code which works with graded modules for a graded algebra and this is what my degree method does -- and is_homogeneous method simply checks to see whether degree() returns False. I think that the function "maximum_degree" must be implemented somewhere. In symmetric functions, this function is called simply "degree". > In cases like symmetric functions, where you are essentially working with polynomials, The behavior should be the same for quasi-symmetric functions and symmetric functions and non-commutative symmetric functions. Quasi-symmetric functions can be considered as polynomials also (if you consider symmetric functions as polynomials) and symmetric functions is a sub algebra of quasi-symmetric functions. In this case non-commutative symmetric functions can also be considered as a subspace of non-commutative polynomials. -Mike On Monday, 13 August 2012 18:18:22 UTC-4, Mike Zabrocki wrote: > > Franco posted this question on the trac server. I thought I would post my > answer here in case there is some discussion. > > > '''Outstanding question about the degree of an element:''' what do we > want > > as the default behaviour? Should it: > > a. raise an error if the element is not homogeneous; or > > b. return the maximum of the degrees of the homogeneous summands? > > The main use that I have for this function is that I want to > sum up to the degree of the symmetric function. In this > usage, the degree should be the maximum (answer: a). > > This is also consistent with what the degree function does > in symmetric functions and that is consistent with the degree > function of polynomials in a single variable. > > -Mike > On Monday, 13 August 2012 18:18:22 UTC-4, Mike Zabrocki wrote: > > Franco posted this question on the trac server. I thought I would post my > answer here in case there is some discussion. > > > '''Outstanding question about the degree of an element:''' what do we > want > > as the default behaviour? Should it: > > a. raise an error if the element is not homogeneous; or > > b. return the maximum of the degrees of the homogeneous summands? > > The main use that I have for this function is that I want to > sum up to the degree of the symmetric function. In this > usage, the degree should be the maximum (answer: a). > > This is also consistent with what the degree function does > in symmetric functions and that is consistent with the degree > function of polynomials in a single variable. > > -Mike > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To view this discussion on the web visit https://groups.google.com/d/msg/sage-combinat-devel/-/ptjUX8tFXXgJ. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
