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Chapter 1.
(cI.tex [1


] [2]) [3]
Chapter 2.
(cLP.tex [4

] [5] [6]
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[][]\OT1/cmr/m/n/10 List of BETA-integers bub-ble sort. \OT1/cmr/m/it/10 Sorts 
a list of atoms into non-descending
 []

[7]) [8]
Chapter 3.
(cAsI.tex [9

]) (cAsIA.tex [10] [11]) (cAsMA.tex [12]) (cAsRA.tex [13]) [14]
Chapter 4.
(cPAsI.tex
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\OT1/cmr/m/it/10 sen-ta-tion \OT1/cmtt/m/n/10 P \OT1/cmr/m/n/10 of a poly-no-mi
al $\OML/cmm/m/it/10 p \OT1/cmr/m/n/10 = [][] \OML/cmm/m/it/10 p[]x[]$ \OT1/cmr
/m/n/10 with $\OML/cmm/m/it/10 e[] > [] > e[]$\OT1/cmr/m/n/10 , $\OML/cmm/m/it/
10 p[] \OMS/cmsy/m/n/10 2 \OT1/cmr/m/n/10 ([] (\OT1/cmr/bx/n/10 D\OT1/cmr/m/n/1
0 [\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 ]) [])[\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/
10 ]$,
 []


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[]\OT1/cmr/m/n/10 The \OT1/cmr/m/it/10 sparse dis-tribu-tive rep-re-sen-ta-tion
 \OT1/cmtt/m/n/10 P \OT1/cmr/m/n/10 of such a poly-no-mial $\OML/cmm/m/it/10 p$
 \OT1/cmr/m/n/10 is the list $(\OT1/cmtt/m/n/10 D[]\OML/cmm/m/it/10 ; \OT1/cmtt
/m/n/10 E[]\OML/cmm/m/it/10 ; \OT1/cmtt/m/n/10 D[]\OML/cmm/m/it/10 ; \OT1/cmtt/
m/n/10 E[]\OML/cmm/m/it/10 ; [] ; \OT1/cmtt/m/n/10 D[]\OML/cmm/m/it/10 ; \OT1/c
mtt/m/n/10 E[]\OT1/cmr/m/n/10 )$,
 []


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\OT1/cmr/m/n/10 where $\OT1/cmtt/m/n/10 D[]$ \OT1/cmr/m/n/10 is the [] in-ter-n
al rep-re-sen-ta-tion of $\OML/cmm/m/it/10 d[]$ \OT1/cmr/m/n/10 and $\OT1/cmtt/
m/n/10 E[]$ \OT1/cmr/m/n/10 is the list $(\OML/cmm/m/it/10 e[]; e[]; [] ; e[]\O
T1/cmr/m/n/10 )$
 []

[15

] [16]) (cPAsPIO.tex [17]
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\OT1/cmr/m/n/10 For $\OML/cmm/m/it/10 r$\OT1/cmr/m/n/10 -variate re-cur-sive po
ly-no-mi-als over $\OT1/cmr/bx/n/10 Q$ \OT1/cmr/m/n/10 the al-go-rithms \OT1/cm
tt/m/n/10 RPREAD \OT1/cmr/m/n/10 and
 []

[18]) (cPAsDIPA.tex [19]
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[][]\OT1/cmr/m/n/10 Polynomial bi-no-mial. \OT1/cmr/m/it/10 Builds $\OML/cmm/m/
it/10 a[]x[] \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 a[]x[]$ \OT1/cmr/m/it/10 from $
\OML/cmm/m/it/10 a[]; a[]; e[]$\OT1/cmr/m/it/10 ,
 []

[20]) (cPAsIPA.tex [21]
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[][]\OT1/cmr/m/n/10 Integral poly-no-mial sub-sti-tu-tion. \OT1/cmr/m/it/10 Sub
-sti-tutes an in-te-gral poly-
 []


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[][]\OT1/cmr/m/n/10 Integral poly-no-mial bi-nary ra-tio-nal eval-u-a-tion, in-
te-gral poly-
 []

[22] [23]
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[][]\OT1/cmr/m/n/10 Integral poly-no-mial trun-ca-tion. \OT1/cmr/m/it/10 Com-pu
tes $\OML/cmm/m/it/10 p [] \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]; [] ; x[]\OT1/
cmr/m/n/10 )$
 []

) (cPAsMPA.tex [24]) (cPAsRPA.tex [25]) (cPAsMR.tex [26]) [27]
Chapter 5.
(cLA.tex [28

]
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[][]\OT1/cmr/m/n/10 Linear dio-phan-tine sys-tem so-lu-tion, mod-i-fied Kan-nan
 and Bachem
 []

[29]) [30]
Chapter 6.
(cGCD.tex [31

] [32] [33]
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[][]\OT1/cmr/m/n/10 Modular uni-vari-ate poly-no-mial great-est com-mon di-vi-s
or. \OT1/cmr/m/it/10 Com-
 []

[34] [35]) [36]
Chapter 7.
(cPF.tex [37

]
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[][]\OT1/cmr/m/n/10 Modular uni-vari-ate poly-no-mial factorization-Berlekamp a
l-go-rithm.
 []


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[][]\OT1/cmr/m/n/10 Integral poly-no-mial mod ideal quadratic Hensel
 []


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[][]\OT1/cmr/m/n/10 Modular poly-no-mial mod ideal, quadratic
 []


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[][]\OT1/cmr/m/n/10 Modular poly-no-mial mod ideal, quadratic Hensel lemma,
 []

[38]
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[][]\OT1/cmr/m/n/10 Modular poly-no-mial dis-tinct de-gree fac-tor-iza-tion. \O
T1/cmr/m/it/10 Given a monic,
 []

) [39]
Chapter 8.
(cRRC.tex [40

] [41] [42]) [43]
Chapter 9.
(cAN.tex [44

] [45] [46] [47]
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[][]\OT1/cmr/m/n/10 Algebraic mod-ule uni-vari-ate poly-no-mial bi-nary ho-mo-t
h-etic trans-
 []

[48]
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[][]\OT1/cmr/m/n/10 Algebraic mod-ule uni-vari-ate poly-no-mial iso-lat-ing in-
ter-vals weakly
 []


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[][]\OT1/cmr/m/n/10 Algebraic mod-ule uni-vari-ate poly-no-mial real
 []

[49]) [50]
Appendix A.
(cCFC.tex [51


] [52] [53] [54] [55]) [56]
Appendix B.
(cISAC.tex
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[] \OT1/cmr/m/n/10 is a small ex-per-i-men-tal in-ter-ac-tive in-ter-face to []
, al-low-ing sim-ple \OT1/cmtt/m/n/10 read--eval--write
 []

[57

] [58] [59]) [60]
Appendix C.
(cNIWsGC.tex (fSPACE.tex) (fLIST.tex) [61

]) [62] (cNIWsCGV.tex [63] [64])
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