Task: Formal power series

C: #include <stdio.h>
#include <stdlib.h>
#include <math.h> 

enum fps_type {
        FPS_CONST = 0,
        FPS_ADD,
        FPS_SUB,
        FPS_MUL,
        FPS_DIV,
        FPS_DERIV,
        FPS_INT,
};

typedef struct fps_t *fps;
typedef struct fps_t {
        int type;
        fps s1, s2;
        double a0;
} fps_t;

fps fps_new()
{
        fps x = malloc(sizeof(fps_t));
        x->a0 = 0;
        x->s1 = x->s2 = 0;
        x->type = 0;
        return x;
}


void fps_redefine(fps x, int op, fps y, fps z)
{
        x->type = op;
        x->s1 = y;
        x->s2 = z;
}

fps _binary(fps x, fps y, int op)
{
        fps s = fps_new();
        s->s1 = x;
        s->s2 = y;
        s->type = op;
        return s;
}

fps _unary(fps x, int op)
{
        fps s = fps_new();
        s->s1 = x;
        s->type = op;
        return s;
}


double term(fps x, int n)
{
        double ret = 0;
        int i;

        switch (x->type) {
        case FPS_CONST: return n > 0 ? 0 : x->a0;
        case FPS_ADD:
                ret = term(x->s1, n) + term(x->s2, n); break;

        case FPS_SUB:
                ret = term(x->s1, n) - term(x->s2, n); break;

        case FPS_MUL:
                for (i = 0; i <= n; i++)
                        ret += term(x->s1, i) * term(x->s2, n - i);
                break;

        case FPS_DIV:
                if (! term(x->s2, 0)) return NAN;

                ret = term(x->s1, n);
                for (i = 1; i <= n; i++)
                        ret -= term(x->s2, i) * term(x, n - i) / term(x->s2, 0);
                break;

        case FPS_DERIV:
                ret = n * term(x->s1, n + 1);
                break;

        case FPS_INT:
                if (!n) return x->a0;
                ret = term(x->s1, n - 1) / n;
                break;

        default:
                fprintf(stderr, "Unknown operator %d\n", x->type);
                exit(1);
        }

        return ret;
}

#define _add(x, y) _binary(x, y, FPS_ADD)
#define _sub(x, y) _binary(x, y, FPS_SUB)
#define _mul(x, y) _binary(x, y, FPS_MUL)
#define _div(x, y) _binary(x, y, FPS_DIV)
#define _integ(x)  _unary(x, FPS_INT)
#define _deriv(x)  _unary(x, FPS_DERIV)

fps fps_const(double a0)
{
        fps x = fps_new();
        x->type = FPS_CONST;
        x->a0 = a0;
        return x;
}

int main()
{
        int i;
        fps one = fps_const(1);
        fps fcos = fps_new();           
        fps fsin = _integ(fcos);        
        fps ftan = _div(fsin, fcos);    

        
        fps_redefine(fcos, FPS_SUB, one, _integ(fsin));

        fps fexp = fps_const(1);        
        
        fps_redefine(fexp, FPS_INT, fexp, 0);

        printf("Sin:");   for (i = 0; i < 10; i++) printf(" %g", term(fsin, i));
        printf("\nCos:"); for (i = 0; i < 10; i++) printf(" %g", term(fcos, i));
        printf("\nTan:"); for (i = 0; i < 10; i++) printf(" %g", term(ftan, i));
        printf("\nExp:"); for (i = 0; i < 10; i++) printf(" %g", term(fexp, i));

        return 0;
}







Python: 

from itertools import islice
from fractions import Fraction
from functools import reduce
try:
    from itertools import izip as zip 
except:
    pass

def head(n):
    
    return lambda seq: islice(seq, n)

def pipe(gen, *cmds):
    
    return reduce(lambda gen, cmd: cmd(gen), cmds, gen)

def sinepower():
    n = 0
    fac = 1
    sign = +1
    zero = 0
    yield zero
    while True:
        n +=1
        fac *= n
        yield Fraction(1, fac*sign)
        sign = -sign
        n +=1
        fac *= n
        yield zero
def cosinepower():
    n = 0
    fac = 1
    sign = +1
    yield Fraction(1,fac)
    zero = 0
    while True:
        n +=1
        fac *= n
        yield zero
        sign = -sign
        n +=1
        fac *= n
        yield Fraction(1, fac*sign)
def pluspower(*powergenerators):
    for elements in zip(*powergenerators):
        yield sum(elements)
def minuspower(*powergenerators):
    for elements in zip(*powergenerators):
        yield elements[0] - sum(elements[1:])
def mulpower(fgen,ggen):
    'From: http://en.wikipedia.org/wiki/Power_series
    a,b = [],[]
    for f,g in zip(fgen, ggen):
        a.append(f)
        b.append(g)
        yield sum(f*g for f,g in zip(a, reversed(b)))
def constpower(n):
    yield n
    while True:
        yield 0
def diffpower(gen):
    'differentiatiate power series'
    next(gen)
    for n, an in enumerate(gen, start=1):
        yield an*n
def intgpower(k=0):
    'integrate power series with constant k'
    def _intgpower(gen):
        yield k
        for n, an in enumerate(gen, start=1):
            yield an * Fraction(1,n)
    return _intgpower


print("cosine")
c = list(pipe(cosinepower(), head(10)))
print(c)
print("sine")
s = list(pipe(sinepower(), head(10)))
print(s)

integc = list(pipe(cosinepower(),intgpower(0), head(10)))

integs1 = list(minuspower(pipe(constpower(1), head(10)),
                          pipe(sinepower(),intgpower(0), head(10))))

assert s == integc, "The integral of cos should be sin"
assert c == integs1, "1 minus the integral of sin should be cos"