1<?xml version="1.0" encoding="UTF-8"?> 2 3<section id="pari"><title>Computer Algebra System PARI</title> 4 5<para>This package offers an &ffi-pac;-based interface to &pari-link;.</para> 6<para>The package <quote role="package">PARI</quote> 7 is &case-sensitive-k;.</para> 8 9<simpara>When this module is present, &features-my; contains the 10 symbol <constant>:PARI</constant>.</simpara> 11 12<para>PARI objects are printed and read using a special 13 <literal role="data">#Z""</literal> syntax.</para> 14 15<para>Most functions accept lisp objects as well as PARI objects and 16return PARI objects, which can be converted to lisp using the 17<function>pari:pari-to-lisp</function> function.</para> 18 19<para>See <filename role="clisp-cvs">modules/pari/test.tst</filename> 20 for sample usage.</para> 21 22<simplesect id="pari-desc"><title>Available functionality</title> 23<para>The module interfaces to most of the functions available in GP, 24by parsing the file <filename>${prefix}/share/pari/pari.desc</filename>, 25see <filename role="clisp-cvs">modules/pari/desc2lisp.lisp</filename>.</para> 26<para>Lisp functions are normally named the same as the GP functions 27they correspond to or the PARI functions they call, e.g.: <itemizedlist> 28<listitem><simpara><function>para:quadpoly</function> corresponds to the 29eponymous GP function and calls the <function>quadpoly0</function> 30PARI function</simpara></listitem> 31<listitem><simpara><function>para:issmall</function> calls the PARI 32function <function>issmall</function> which has no GP 33analogue</simpara></listitem> 34<listitem><simpara><function>para:random_</function> (note the 35<literal>_</literal> suffix to avoid clash with the &ansi-cl; &random;) 36corresponds to the GP function <function>random</function> and calls the 37<function>genrand</function> PARI function.</simpara></listitem></itemizedlist> 38</para></simplesect> 39 40<simplesect id="pari-ext"><title>Extending the module</title> 41<para>Not all PARI functions have a corresponding Lisp function, but one can 42remedy that with just a few lines: <programlisting language="lisp"> 43(&default-foreign-library; "libpari.so") ; or pari.dll on &win32; 44(pari:pari-call-out (matrix-rank ffi:long) "rank" (x))<lineannotation>long rank(GEN x);</lineannotation> 45(pari:pari-call-out fibonacci "fibo" ((n ffi:long)))<lineannotation>GEN fibo(long n);</lineannotation> 46(pari:pari-call-out-prec pari-arctan "gatan" (x))<lineannotation>GEN gatan(GEN x, long prec);</lineannotation> 47(pari:pari-call-out (equal? boolean) "gequal" (x y))<lineannotation>GEN gequal(GEN x, GEN y);</lineannotation> 48</programlisting> 49(Actually, these four functions are already interfaced to by the module.) 50Please feel free to submit additions for 51 <filename role="clisp-cvs">modules/pari/pari.lisp</filename> 52 and <filename role="clisp-cvs">modules/pari/test.tst</filename>.</para> 53</simplesect> 54 55<simplesect id="pari-prec"><title>Real precision</title> 56<para>The real precision defaults to <varname>pari:pari-real-precision</varname> 57which specifies the default precision in decimal digits: 58<programlisting language="lisp"> 59pari:pari-real-precision 60<computeroutput>19</computeroutput> 61(&length; (&prin1-to-string; (pari:pari-to-lisp (pari:Pi)))) 62<computeroutput>23</computeroutput> 63</programlisting> 64One can also pass the precision parameter explicitly: 65<programlisting language="lisp"> 66(&length; (&prin1-to-string; (pari:pari-to-lisp (pari:Pi :prec 38)))) 67<computeroutput>41</computeroutput> 68</programlisting> 69Note that the <emphasis>actual</emphasis> precision is determined by the 70size of the mantissa which can be incremented only in steps of 71<code>(&bitsizeof; 'ffi:ulong)</code> (64 bits or 32 bits).</para> 72</simplesect> 73</section> 74