can be represented as a list of reals
![\( [a_0, a_1, \ldots, a_n] \)](homework4-img2.png){kind=small}
.
Write functions eval, pow and polyToString so
that we can evaluate:
A polynomial
can be represented as a list of reals
.
Write functions eval, pow and polyToString so
that we can evaluate:
- val p = [1.0,2.0]; (* 2x + 1 *) val p = [1.0,2.0] : real list - eval(p,0.1); val it = 1.2 : real - val p3 = pow(3,p); val p3 = [1.0,6.0,12.0,8.0] : real list - eval(p3,0.1); val it = 1.728 : real - polyToString(p3); val it = "8.0x^3 + 12.0x^2 + 6.0x + 1.0" : string - polyToString [0.0,0.0,~1.0,0.0,0.0]; val it = "0.0x^4 + 0.0x^3 + ~1.0x^2 + 0.0x + 0.0" : string - polyToString [0.0]; val it = "0.0" : string - polyToString []; val it = "0.0" : stringYou will need to use the functions
Real.toString and
Int.toString to get strings for numbers. Don't ``open'' either
the ``Real'' or the ``Int'' structure because it will cause
overloading functions to misbehave.
Do not use if in any of your code for polynomials.
Put the resulting functions in poly.sml in your AFS
homework4 folder.
Our solution uses four additional functions, three of them at the
top-level (useful named functions), and one a helper for the
polyToString function.
Do Exercises 3 and 4 of Chapter 8 (page 131).
Leave poly.sml in your AFS folder. Turn in the book exercises
on paper at the beginning of lecture.