$SPAD/src/input liu.input

Xiaojun Liu December 3, 2016

Abstract

This makes it clear that the exponential operation semantics is different for the use of “^” and “**” in some cases.

Contents

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Does exponential operation “^” and “**” of a differential operator, say L, means repeating multiplications of L in Axiom ? If so, it seems the following code produced an unexpected result:

— * —

)set break resume
)spool liu.output
)set message test on
)set message auto off
)set message type off
)clear all
--S 1 of 9
Dx: LODO(EXPR INT, f+->D(f,x)) := D()
--R
--R   (1)  D
--E 1
--S 2 of 9
u := operator 'u
--R
--R   (2)  u
--E 2
--S 3 of 9
L := Dx + u(x)
--R
--R   (3)  D + u(x)
--E 3
--S 4 of 9
L**2 = L*L
--R
--R         2                2   2             ,          2
--R   (4)  D  + 2u(x)D + u(x) = D  + 2u(x)D + u (x) + u(x)
--R
--E 4
)clear all
--S 5 of 9
f: INT->INT:=x+->x+1
--R
--R   (1)  theMap(Closure)
--E 5
--S 6 of 9
K := OREUP ( x, INT, 1, f);
--R

--E 6
--S 7 of 9
x:K
--E 7
--S 8 of 9
L:=x+1
--R
--R   (4)  x + 1
--E 8
--S 9 of 9
L^2=L*L
--R
--R         2            2
--R   (5)  x  + 2x + 1= x  + 4x + 3
--E 9
)spool
)lisp (bye)

———-

Clearly, the r.h.s. is correct too. I checked the .spad file, it seems the exponential operation of LODO (or its parent OREUP) is missed (or I guess it is directly inherited as usual polynomial operation). However I am not clever enough to modify the code. Please check this, thanks.

References^{[1] nothing}

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