Multiplying Big-Ints in scheme-racket

I've implemented a "big-int" in scheme as a list, so the first element is the sign of the number (+ or -) and the following are the value of the number itself, first the ones, then the tens etc.

For example: (+ 0 0 1) is for 100, (- 9 2 3 1) is for -1329 etc.

What I need now is to implement addition, subtraction and multiplication for big-ints implemented in this manner. I've done addition and subtraction, can someone help me with multiplication, please?


Break the problem up into smaller pieces. First, write a function that multiplies a Big-int by a single digit. Then, extend this (using Greg Hewgill's hint that you probably know how to do this on paper) to a function that multiplies a Big-int by a list of digits. Finally, wrap this in a function that accepts two Big-ints, strips off the sign, and then calls your previous function.

I strongly suggest that you write test cases for these functions before developing them.

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