\$\texttt{Apart}: a generalized \textsc{Mathematica} \texttt{Apart} function

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Abstract: We have generalized the extsc{Mathematica} function exttt{Apart} from 1 to

N

dimension, the generalized function exttt{

mathcal{V}_{x}^*

t o i r r e d u c i b l e o n e s . T h e e l e m e n t s i n

mathcal{V}_{x}^*

c a n b e v i e w e d a s t h e c o r r e s p o n d i n g p r o p a g a t o r s w h i c h i n v o l v e l o o p m o m e n t a, a n d t h e d e c o m p o s i t i o n w i l l b e u s e f u l w h e n o n e t r i e s t o p e r f o r m t h e l o o p c a l c u l a t i o n s u s i n g t h e p a c k a g e s s u c h a s e x t s c F i r e a n d e x t s c R e d u z e, w h i c h h a v e i m p l e m e n t e d t h e i n t e g r a t i o n b y p a r t s (I B P) i d e n t i t i e s a n d L o r e n t z i n v a r i a n c e (L I) i d e n t i t i e s . A d e s c r i p t i o n o n h o w t o u s e t h i s p a c k a g e, c o m b i n e d w i t h e x t s c F i r e, e x t s c F e y n A r t s a n d e x t s c F e y n C a l c p a c k a g e s, t o d o t h e o n e - l o o p c a l c u l a t i o n s i n d o u b l e q u a r k o n i u m p r o d u c t i o n i n

e^+e^-

c o l l i d e r s i s g i v e n, a n d t h e f u l l s o u r c e c o d e f o r a s p e c i f i c p r o c e s s

(e^+e^- o J/psi + eta_c)$ is also available.

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