$SPAD/src/input lodo1.input

Timothy Daly December 3, 2016

Abstract

Contents

2

1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)set break resume
)spool lodo1.output
)set message test on
)set message auto off
)clear all
--S 1 of 20
RFZ := Fraction UnivariatePolynomial('x, Integer)
--R
--R
--R   (1)  Fraction(UnivariatePolynomial(x,Integer))
--R                                                                 Type: Domain
--E 1
--S 2 of 20
x : RFZ := 'x
--R
--R
--R   (2)  x
--R                              Type: Fraction(UnivariatePolynomial(x,Integer))
--E 2
--S 3 of 20
Dx : LODO1 RFZ := D()
--R
--R
--R   (3)  D
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 3
--S 4 of 20
b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x
--R
--R
--R          2 2        1
--R   (4)  3x D  + 2D + -
--R                     x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 4
--S 5 of 20

a : LODO1 RFZ := b*(5*x*Dx + 7)
--R
--R
--R           3 3       2        2         7
--R   (5)  15x D  + (51x  + 10x)D  + 29D + -
--R                                        x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 5
--S 6 of 20
p := x**2 + 1/x**2
--R
--R
--R         4
--R        x  + 1
--R   (6)  ------
--R           2
--R          x
--R                              Type: Fraction(UnivariatePolynomial(x,Integer))
--E 6
--S 7 of 20
(a*b - b*a) p
--R
--R
--R             4
--R        - 75x  + 540x - 75
--R   (7)  ------------------
--R                 4
--R                x
--R                              Type: Fraction(UnivariatePolynomial(x,Integer))
--E 7
--S 8 of 20
ld := leftDivide(a,b)
--R
--R
--R   (8)  [quotient= 5x D + 7,remainder= 0]
--IType: Record(quotient: LinearOrdinaryDifferentialOperator1(...
--E 8
--S 9 of 20
a = b * ld.quotient + ld.remainder
--R
--R
--R           3 3       2        2         7     3 3       2        2         7
--R   (9)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                        x                                  x
--IType: Equation(LinearOrdinaryDifferentialOperator1(...
--E 9

--S 10 of 20
rd := rightDivide(a,b)
--R
--R
--R                                              5
--R   (10)  [quotient= 5x D + 7,remainder= 10D + -]
--R                                              x
--IType: Record(quotient: LinearOrdinaryDifferentialOperator1(...
--E 10
--S 11 of 20
a = rd.quotient * b + rd.remainder
--R
--R
--R            3 3       2        2         7     3 3       2        2         7
--R   (11)  15x D  + (51x  + 10x)D  + 29D + -= 15x D  + (51x  + 10x)D  + 29D + -
--R                                         x                                  x
--IType: Equation(LinearOrdinaryDifferentialOperator1(Fraction(...
--E 11
--S 12 of 20
rightQuotient(a,b)
--R
--R
--R   (12)  5x D + 7
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 12
--S 13 of 20
rightRemainder(a,b)
--R
--R
--R               5
--R   (13)  10D + -
--R               x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 13
--S 14 of 20
leftExactQuotient(a,b)
--R
--R
--R   (14)  5x D + 7
--IType: Union(LinearOrdinaryDifferentialOperator1(...
--E 14
--S 15 of 20
e := leftGcd(a,b)
--R

--R
--R           2 2        1
--R   (15)  3x D  + 2D + -
--R                      x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 15
--S 16 of 20
leftRemainder(a, e)
--R
--R
--R   (16)  0
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 16
--S 17 of 20
rightRemainder(a, e)
--R
--R
--R               5
--R   (17)  10D + -
--R               x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 17
--S 18 of 20
f := rightLcm(a,b)
--R
--R
--R            3 3       2        2         7
--R   (18)  15x D  + (51x  + 10x)D  + 29D + -
--R                                         x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 18
--S 19 of 20
rightRemainder(f, b)
--R
--R
--R               5
--R   (19)  10D + -
--R               x
--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 19
--S 20 of 20
leftRemainder(f, b)
--R
--R
--R   (20)  0

--IType: LinearOrdinaryDifferentialOperator1(Fraction(...
--E 20
)spool
)lisp (bye)

———-

References^{[1] nothing}

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