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## [Axiom-developer] [AxiomProblems] Yet another problem with piecewise fun

**From**: |
anonymous |

**Subject**: |
[Axiom-developer] [AxiomProblems] Yet another problem with piecewise functions |

**Date**: |
Mon, 14 Mar 2005 16:18:17 -0600 |

Changes http://page.axiom-developer.org/zope/mathaction/AxiomProblems/diff
--
Consider the following function, given in recursive manner:
\begin{axiom}
N0(t|(t<0) or (t>1))==0
N0(t|(t>=0) and (t<=1))==1
N(t,i,0)==N0(t-i)
N(t,i,p|p>0)==(t-i)/p*N(t,i,p-1)+(i+1-t)/p*N(t,i+1,p-1)
\end{axiom}
This is a way to create (uniform) bsplines. Now try to differentiate $N$
\begin{axiom}
D(N(t,0,3),t)
\end{axiom}
Yack!!! This is obviously wrong!!! $t\mapsto N(t,0,3)$ is $C^2$ continuous!
--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden

**[Axiom-developer] [AxiomProblems] Yet another problem with piecewise functions**,
*anonymous* **<=**