我想要得到如下的多项式长除法：
但是如您所知，当我使用命令\polylongdiv（包polynom）时，我总是得到以下信息：
我怎样才能得到第一张图片中的结果？目前，我不知道该怎么做。这是我的 tex 文件：
\documentclass{article}
\usepackage{polynom}
\begin{document}
$$\polylongdiv{x^3-12x^2-42}{x-3}$$
\end{document}
答案1
不久前，我尝试重新实现多项式长除法，因为我想要一些类似的东西。
另存为polydiv.sty
\ProvidesPackage{polydiv}
\RequirePackage{xparse,expl3}
\ExplSyntaxOn
\bool_new:N \l__poly_zeros_bool
\bool_new:N \l__poly_first_bool
\bool_new:N \l__poly_trailing_bool
\bool_new:N \l__poly_ptrailing_bool
\bool_new:N \l__poly_stage_bool
\bool_set_true:N \l__poly_stage_bool
\tl_new:N \l__poly_var_tl
\tl_new:N \l__poly_sep_tl
\tl_new:N \l__poly_longdiv_sep_tl
\tl_new:N \l__poly_oline_tl
\tl_new:N \l__poly_uline_tl
\tl_set:Nn \l__poly_var_tl {x}
\tl_set:Nn \l__poly_sep_tl {}
\tl_set:Nn \l__poly_longdiv_sep_tl {}
\int_new:N \l__poly_deg_int
\int_new:N \l__poly_pad_int
\int_new:N \l__poly_tmpa_int
\int_new:N \l__poly_tmpb_int
\int_new:N \l__poly_trailing_int
\int_new:N \l__poly_stage_int
\int_new:N \l__poly_cstage_int
\int_set:Nn \l__poly_pad_int{3}
\seq_new:N \l__poly_gtmpa_seq
\keys_define:nn { polynomial }
{
stage .code:n = {
\bool_set_false:N \l__poly_stage_bool
\int_set:Nn \l__poly_stage_int {#1}
},
zeros .bool_set:N = \l__poly_zeros_bool,
separator .tl_set:N = \l__poly_sep_tl,
variable .tl_set:N = \l__poly_var_tl,
var .tl_set:N = \l__poly_var_tl,
% trailing .bool_set:N = \l__poly_trailing_bool
}
\cs_new_nopar:Npn \poly_print:N #1 {
\int_gset:Nn \l__poly_deg_int {\seq_count:N #1}
\int_gdecr:N \l__poly_deg_int
\int_gset:Nn \l__poly_tmpa_int {\l__poly_deg_int -
\l__poly_trailing_int+1}
\bool_gset_eq:NN \l__poly_ptrailing_bool \l__poly_trailing_bool
\bool_gset_true:N \l__poly_first_bool
\int_compare:nT {\l__poly_deg_int < \l__poly_pad_int} {
\prg_replicate:nn {2*(\l__poly_pad_int -
\l__poly_deg_int)}{\tl_use:N \l__poly_sep_tl}
}
\seq_map_inline:Nn #1 {
\bool_if:nTF {\int_compare_p:n {##1 == 0} && \l__poly_first_bool}
{
\tl_use:N \l__poly_sep_tl
\tl_use:N \l__poly_sep_tl
}
{
\bool_if:nTF {\int_compare_p:n {##1 != 0} || \l__poly_zeros_bool}
{
\int_compare:nTF {##1 < 0}
{
\bool_if:NF \l__poly_first_bool {
\tl_use:N \l__poly_sep_tl
}
- \tl_use:N \l__poly_sep_tl
\bool_if:nF {\int_compare_p:n {##1 == -1} && \int_compare_p:n {\l__poly_deg_int > 0}}
{
\int_eval:n {-##1}
}
}
{
\bool_if:NF \l__poly_first_bool {\tl_use:N \l__poly_sep_tl+} \tl_use:N \l__poly_sep_tl
\bool_if:nF {\int_compare_p:n {##1 == 1} && \int_compare_p:n {\l__poly_deg_int > 0}}
{
##1
}
}
\int_compare:nT {\l__poly_deg_int > 0}
{
\tl_use:N \l__poly_var_tl
\int_compare:nT {\l__poly_deg_int > 1} {^{\int_use:N \l__poly_deg_int}}
}
}
{
\tl_use:N \l__poly_sep_tl
\tl_use:N \l__poly_sep_tl
}
\bool_gset_false:N \l__poly_first_bool
}
\int_gdecr:N \l__poly_deg_int
\bool_if:nT {\l__poly_ptrailing_bool && \int_compare_p:n {\l__poly_deg_int < \l__poly_tmpa_int}} {
\seq_map_break:
}
}
}
\cs_generate_variant:Nn \poly_print:N {c}
\cs_new_nopar:Npn \poly_add:NNN #1#2#3 {
\seq_clear_new:N #1
\int_step_inline:nnnn {1} {1} {\int_max:nn {\seq_count:N #2} {\seq_count:N #3}} {
\seq_put_left:Nx #1 {\int_eval:n {\seq_item:Nn #2 { - ##1} + \seq_item:Nn #3 { - ##1}+0}}
}
}
\cs_generate_variant:Nn \poly_add:NNN {Ncc,ccc}
\cs_new_nopar:Npn \poly_sub:NNN #1#2#3 {
\seq_clear_new:N #1
\int_step_inline:nnnn {1} {1} {\int_max:nn {\seq_count:N #2} {\seq_count:N #3}} {
\seq_put_left:Nx #1 {\int_eval:n {\seq_item:Nn #2 { - ##1} - \seq_item:Nn #3 { - ##1}+0}}
}
}
\cs_generate_variant:Nn \poly_sub:NNN {Ncc,ccc}
\cs_new_nopar:Npn \poly_shift:Nn #1#2 {
\prg_replicate:nn {#2} {
\seq_put_right:Nn #1 {0}
}
}
\cs_new_nopar:Npn \poly_mul:NNN #1#2#3 {
\seq_clear_new:N #1
\group_begin:
\seq_clear_new:N \l__poly_tmpa_seq
\seq_clear_new:N \l__poly_tmpb_seq
\seq_clear_new:N \l__poly_tmpc_seq
\int_set:Nn \l__poly_tmpa_int {\seq_count:N #2 - 1}
\seq_map_inline:Nn #2 {
\seq_clear:N \l__poly_tmpa_seq
\seq_map_inline:Nn #3 {
\seq_put_right:Nx \l__poly_tmpa_seq {\int_eval:n {##1 * ####1}}
}
\poly_shift:Nn \l__poly_tmpa_seq {\l__poly_tmpa_int}
\poly_add:NNN \l__poly_tmpc_seq \l__poly_tmpb_seq \l__poly_tmpa_seq
\seq_set_eq:NN \l__poly_tmpb_seq \l__poly_tmpc_seq
\int_decr:N \l__poly_tmpa_int
}
\seq_gset_eq:NN \l__poly_gtmpa_seq \l__poly_tmpb_seq
\group_end:
\seq_set_eq:NN #1 \l__poly_gtmpa_seq
\seq_clear:N \l__poly_gtmpa_seq
}
\cs_generate_variant:Nn \poly_mul:NNN {Ncc, ccc}
\cs_new_nopar:Npn \poly_div:NNN #1#2#3 {
\seq_clear_new:N #1
\seq_put_left:Nx #1 {\int_eval:n {\seq_item:Nn #2 {1} / \seq_item:Nn #3 {1}}}
\poly_shift:Nn #1 {\seq_count:N #2 - \seq_count:N #3}
}
\cs_generate_variant:Nn \poly_div:NNN {Ncc, ccc}
\prg_new_conditional:Npnn \poly_is_divisible:NN #1#2 {p,T,F,TF} {
\int_compare:nTF {\seq_count:N #1 < \seq_count:N #2}
{
\prg_return_false:
}
{
\prg_return_true:
}
}
\cs_new_nopar:Npn \poly_trim:N #1 {
\bool_do_while:nn {\int_compare_p:n {\seq_item:Nn #1 {1} == 0}} {
\seq_pop_left:NN #1 \l_tmpa_tl
}
}
\cs_new_nopar:Npn \poly_longdiv:NN #1#2 {
\group_begin:
\seq_clear_new:N \l__poly_quotient_seq
\seq_clear_new:N \l__poly_remainder_seq
\seq_clear_new:N \l__poly_factor_seq
\seq_set_eq:NN \l__poly_remainder_seq #1
\seq_clear_new:N \l__poly_lines_seq
\int_zero:N \l__poly_cstage_int
\bool_do_while:nn {
\poly_is_divisible_p:NN \l__poly_remainder_seq #2
&&
(\l__poly_stage_bool || \int_compare_p:n {\l__poly_stage_int > \l__poly_cstage_int})
}
{
\poly_div:NNN \l__poly_factor_seq \l__poly_remainder_seq #2
\poly_add:NNN \l__poly_tmpa_seq \l__poly_factor_seq \l__poly_quotient_seq
\seq_set_eq:NN \l__poly_quotient_seq \l__poly_tmpa_seq
\poly_mul:NNN \l__poly_tmpa_seq \l__poly_factor_seq #2
\seq_put_right:NV \l__poly_lines_seq \l__poly_tmpa_seq
\int_incr:N \l__poly_cstage_int
\bool_if:nT {\l__poly_stage_bool || \int_compare_p:n
{\l__poly_stage_int > \l__poly_cstage_int}}
{
\poly_sub:NNN \l__poly_tmpb_seq \l__poly_remainder_seq \l__poly_tmpa_seq
\seq_set_eq:NN \l__poly_remainder_seq \l__poly_tmpb_seq
\poly_trim:N \l__poly_remainder_seq
\seq_put_right:NV \l__poly_lines_seq \l__poly_remainder_seq
\int_incr:N \l__poly_cstage_int
}
}
\int_set:Nn \l__poly_pad_int {\seq_count:N #1 + \seq_count:N
#2-1}
\tl_set:Nn \l__poly_sep_tl {&}
\tl_set:Nn \l__poly_longdiv_sep_tl {\cr}
\bool_set_true:N \l__poly_zeros_bool
\int_set:Nn \l__poly_tmpa_int {2*\seq_count:N #1+1}
\tl_set:Nn \l__poly_oline_tl {\multispan}
\tl_put_right:Nx \l__poly_oline_tl {{\int_use:N \l__poly_tmpa_int}}
\tl_put_right:Nn \l__poly_oline_tl {\hrulefill\cr}
\tl_set:Nn \l__poly_uline_tl {\multispan}
\tl_put_right:Nx \l__poly_uline_tl {{\int_eval:n {2*\seq_count:N #2 - 1}}}
\tl_put_right:Nn \l__poly_uline_tl {\hrulefill\cr}
\int_set:Nn \l__poly_trailing_int {\seq_count:N #2}
\leavevmode\vbox{\halign { $##$&&$\>##$ \crcr
&
\bool_if:NTF \l__poly_stage_bool
{
\bool_set_false:N \l__poly_trailing_bool
}
{
\bool_set_true:N \l__poly_trailing_bool
\int_set:Nn \l__poly_trailing_int {\l__poly_stage_int/2}
}
\poly_print:N \l__poly_quotient_seq
\tl_use:N \l__poly_longdiv_sep_tl
\noalign{\vskip-\normalbaselineskip\vskip\jot}
\prg_replicate:nn {2*\seq_count:N #2} {&}
\tl_use:N \l__poly_oline_tl
\int_set:Nn \l__poly_pad_int {0}
\bool_set_true:N \l__poly_trailing_bool
\poly_print:N #2
&
\smash{\Bigr)}
&
\int_set:Nn \l__poly_pad_int {0}
\bool_set_false:N \l__poly_trailing_bool
\poly_print:N #1
\tl_use:N \l__poly_longdiv_sep_tl
\int_gzero:N \l__poly_tmpb_int
\seq_map_inline:Nn \l__poly_lines_seq {
\tl_gset:Nn \l__poly_tmpa_seq {##1}
\int_gincr:N \l__poly_tmpb_int
&
\bool_set_true:N \l__poly_trailing_bool
\poly_print:N \l__poly_tmpa_seq
\bool_if:nT {\int_compare_p:n
{\int_mod:nn{\l__poly_tmpb_int}{2} == 1} &&
\int_compare_p:n {
\l__poly_tmpb_int < 2*(\seq_count:N #1 - \seq_count:N #2)
}
&&
\int_compare_p:n {
\l__poly_tmpb_int != \seq_count:N \l__poly_lines_seq
}
} {
&&\hfill\downarrow\hfill
}
\tl_use:N \l__poly_longdiv_sep_tl
\int_compare:nT {\int_mod:nn{\l__poly_tmpb_int}{2} == 1} {
\noalign{\vskip-\normalbaselineskip\vskip\jot}
\prg_replicate:nn {2*\seq_count:N #2 + \l__poly_tmpb_int + 1} {&}
\tl_use:N \l__poly_uline_tl
}
}
\cr
}}
\group_end:
}
\cs_generate_variant:Nn \poly_longdiv:NN {cc}
\NewDocumentCommand \PolyPrint { O{} m } {
\group_begin:
\keys_set:nn { polynomial }
{
#1
}
\poly_print:c {polynomial #2}
\group_end:
}
\NewDocumentCommand \PolySet { m m } {
\seq_set_from_clist:cn {polynomial #1} {#2}
}
\NewDocumentCommand \PolyLongDiv {O{} m m } {
\group_begin:
\keys_set:nn { polynomial }
{
#1
}
\poly_longdiv:cc {polynomial #2} {polynomial #3}
\group_end:
}
\ExplSyntaxOff
然后执行以下操作：
\documentclass{article}
%\url{http://tex.stackexchange.com/q/79411/86}
\usepackage{polydiv}
\begin{document}
\PolySet{a}{1,-12,0,-42}
\PolySet{b}{1,-3}
\(\PolyLongDiv{a}{b}\)
\end{document}
生成：
