'*****************************************************
'*  This program calculates R(x) = a*P(x) + b*Q(x),  *
'*  P(x), Q(x) and R(x) being polynomials.           *
'* ------------------------------------------------- *
'* Ref.: "Mathematiques en Turbo-Pascal By M. Ducamp *
'* and A. Reverchon (vol 2), Eyrolles, Paris, 1988"  *
'* [BIBLI 05].                                       *
'* ------------------------------------------------- *
'* SAMPLE RUN:                                       *
'*                                                   *
'* LINEAR COMBINATION OF TWO POLYNOMIALS:            *
'*                                                   *
'* P(X) = x3 +5/4x2 -8                               *
'* Q(x) = 2x2 -1/7                                   *
'*                                                   *
'* a = 1/2                                           *
'* b = -1/3                                          *
'*                                                   *
'*                                                   *
'* + 1 / 2 X3 - 1 / 24 X2 - 83 / 21                  *
'*                                                   *
'*                                                   *
'*                     BASIC version by J-P Moreau.  *
'*                          (www.jpmoreau.fr)        *
'*****************************************************
defdbl a-h,o-z
defint i-n

MAXINT = 32767  'Maximum integer number
MAXPOL = 20     'Maximum degree for a polynomial
SMALL  = 1e-20  'small real number

' number zz (real, integer or fractional)
' isrzz=1: zz is real (double precision)
' isrzz=0: zz is integer or fractional
' zzv:  value of zz if real
' ipzz: integer value of zz if integer (or numerator value if fractional)
' iqzz: denominator value if fractional (=1 if integer)

'a polynomial P is defined by:
'integer ipdeg (degree of polynomial)
'number  cp(MAXPOL) (coefficients of polynomial, real, integer or fractional)

'predefine 3 polynomials P,Q,R
DIM isrcp(MAXPOL),cpv(MAXPOL),ipcp(MAXPOL),iqcp(MAXPOL)
DIM isrcq(MAXPOL),cqv(MAXPOL),ipcq(MAXPOL),iqcq(MAXPOL)
DIM isrcr(MAXPOL),crv(MAXPOL),ipcr(MAXPOL),iqcr(MAXPOL)

cls
print
print " LINEAR COMBINATION OF TWO POLYNOMIALS:"
print
tx$=" P(x) = ": gosub 4000 'Enter P(x)
'put P(x) in R(x)
irdeg=ipdeg
for i=0 to ipdeg
  isrcr(i)=isrcp(i)
  crv(i)=cpv(i)
  ipcr(i)=ipcp(i)
  iqcr(i)=iqcp(i)
next i
tx$=" Q(x) = ": gosub 4000 'Enter P(x)
'put P(x) in Q(x)
iqdeg=ipdeg
for i=0 to ipdeg
  isrcq(i)=isrcp(i)
  cqv(i)=cpv(i)
  ipcq(i)=ipcp(i)
  iqcq(i)=iqcp(i)
next i
'restore P(x)
ipdeg=irdeg
for i=0 to irdeg
  isrcp(i)=isrcr(i)
  cpv(i)=crv(i)
  ipcp(i)=ipcr(i)
  iqcp(i)=iqcr(i)
next i
print
'read number a
input " a = ", ch$: gosub 1000  'zz=SetNumber(ch$)
'put zz in a
isra=isrzz:av=zzv:ipa=ipzz:iqa=iqzz
'read number b
input " b = ", ch$: gosub 1000  'zz=SetNumber(ch$)
'put zz in b
isrb=isrzz:bv=zzv:ipb=ipzz:iqb=iqzz

gosub 500   'R(x)=CombiPolynom(P,Q,a,b)

if IERROR<>0 then
  print " Error in combination."
else
  'put R(x) in P(x) for printing
  ipdeg=irdeg
  for i=0 to irdeg
    isrcp(i)=isrcr(i)
    cpv(i)=crv(i)
    ipcp(i)=ipcr(i)
    iqcp(i)=iqcr(i)
  next i
  print
  gosub 5000  'display P(x)
end if

END


' a P(X) + b Q(X) = R(X)
'CombiPolynom
'u,v: NUMBER
500 IERROR=0
if iqdeg > ipdeg then
  irdeg=iqdeg
else
  irdeg=ipdeg
end if
if irdeg > MAXPOL then
  IERROR=1
  return   'degree of R(x) is too big
end if
for i=0 to irdeg
  'set u and v to zero
  isru=0:uv=0#:ipu=0:iqu=1
  isrv=0:vv=0#:ipv=0:iqv=1
  if i<=ipdeg then
    'MultNumber(a,P.coeff[i], u)
    isrxx=isra:xxv=av:ipxx=ipa:iqxx=iqa                 'xx=a
    isryy=isrcp(i):yyv=cpv(i):ipyy=ipcp(i):iqyy=iqcp(i) 'yy=P coeff(i)
    gosub 3100                                          'zz=xx*yy
    isru=isrzz:uv=zzv:ipu=ipzz:iqu=iqzz                 'u=zz
  end if
  if i<=iqdeg then
    'MultNumber(b,Q.coeff[i], v)
    isrxx=isrb:xxv=bv:ipxx=ipb:iqxx=iqb                 'xx=b
    isryy=isrcq(i):yyv=cqv(i):ipyy=ipcq(i):iqyy=iqcq(i) 'yy=Q coeff(i)
    gosub 3100                                          'zz=xx*yy
    isrv=isrzz:vv=zzv:ipv=ipzz:iqv=iqzz                 'v=zz
  end if
  'AddNumber(u,v,R.coeff[i])
  isrxx=isru:xxv=uv:ipxx=ipu:iqxx=iqu                   'xx=u
  isryy=isrv:yyv=vv:ipyy=ipv:iqyy=iqv                   'yy=v
  gosub 3000                                            'zz=xx+yy
  isrcr(i)=isrzz:crv(i)=zzv:ipcr(i)=ipzz:iqcr(i)=iqzz   'R coeff(i)=zz
next i
510 if irdeg<=0 or abs(crv(irdeg))>SMALL then goto 520
  irdeg=irdeg-1
  goto 510
520 return


$INCLUDE "Numeric\Polynoms\polynoms.bas"

'end of file combipol.bas