Update readme

poly/README.md

@@ -20,7 +20,10 @@ using Horner's method for stability.
 fn eval(c []f64, x f64) f64
 ```
 
-This function evaluates a polynomial with real coefficients for the real variable `x`.
+This function evaluates a polynomial and its derivatives storing the
+results in the array `res` of size `lenres`. The output array
+contains the values of `d^k P(x)/d x^k` for the specified value of
+`x` starting with `k = 0`.
 
 ```v ignore
 fn eval_derivs(c []f64, x f64, lenres u64) []f64
@@ -40,9 +43,22 @@ This function finds the real roots of the quadratic equation,
 a x^2 + b x + c = 0
 ```
 
-The number of real roots (either zero, one, or two) is returned, and their locations are returned as `[ x0, x1 ]`. If no real roots are found then `[]` is returned. If one real root is found (i.e., if `a=0`), it is returned as `[ x0 ]`. When two real roots are found, they are returned as `[ x0, x1 ]` in ascending order. The case of coincident roots is not considered special. For example, `(x-1)^2=0` will have two roots, which happen to have exactly equal values.
+The number of real roots (either zero, one or two) is returned, and
+their locations are are returned as `[ x0, x1 ]`. If no real roots
+are found then `[]` is returned. If one real root
+is found (i.e. if `a=0`) then it is are returned as `[ x0 ]`. When two
+real roots are found they are are returned as `[ x0, x1 ]` in
+ascending order. The case of coincident roots is not considered
+special. For example `(x-1)^2=0` will have two roots, which happen
+to have exactly equal values.
 
-The number of roots found depends on the sign of the discriminant `b^2 - 4 a c`. This will be subject to rounding and cancellation errors when computed in double precision, and will also be subject to errors if the coefficients of the polynomial are inexact. These errors may cause a discrete change in the number of roots. However, for polynomials with small integer coefficients, the discriminant can always be computed exactly.
+The number of roots found depends on the sign of the discriminant
+`b^2 - 4 a c`. This will be subject to rounding and cancellation
+errors when computed in double precision, and will also be subject to
+errors if the coefficients of the polynomial are inexact. These errors
+may cause a discrete change in the number of roots. However, for
+polynomials with small integer coefficients the discriminant can always
+be computed exactly.
 
 ## Cubic Equations
 
@@ -56,7 +72,16 @@ This function finds the real roots of the cubic equation,
 x^3 + a x^2 + b x + c = 0
 ```
 
-with a leading coefficient of unity. The number of real roots (either one or three) is returned, and their locations are returned as `[ x0, x1, x2 ]`. If one real root is found, only `[ x0 ]` is returned. When three real roots are found, they are returned as `[ x0, x1, x2 ]` in ascending order. The case of coincident roots is not considered special. For example, the equation `(x-1)^3=0` will have three roots with exactly equal values. As in the quadratic case, finite precision may cause equal or closely-spaced real roots to move off the real axis into the complex plane, leading to a discrete change in the number of real roots.
+with a leading coefficient of unity. The number of real roots (either
+one or three) is returned, and their locations are returned as `[ x0, x1, x2 ]`.
+If one real root is found then only `[ x0 ]`
+is returned. When three real roots are found they are returned as
+`[ x0, x1, x2 ]` in ascending order. The case of
+coincident roots is not considered special. For example, the equation
+`(x-1)^3=0` will have three roots with exactly equal values. As
+in the quadratic case, finite precision may cause equal or
+closely-spaced real roots to move off the real axis into the complex
+plane, leading to a discrete change in the number of real roots.
 
 ## Companion Matrix