Fix CLI I/O: reject malformed input and stop labeling unlifted GBs as char 0

Makefile.am

@@ -65,6 +65,7 @@ checkdiff               = test/diff/diff_bug-2nd-prime-bad.sh \
 			  test/diff/diff_quadratic-nonradical-qq.sh \
 			  test/diff/diff_radical-shape-31.sh \
 			  test/diff/diff_radical-shape-qq.sh \
+			  test/diff/diff_reject-malformed.sh \
 			  test/diff/diff_realroot1.sh \
 			  test/diff/diff_realroot-extraction-exact-root.sh \
 			  test/diff/diff_reals-dim0-chgvar.sh \

README.md

@@ -47,11 +47,13 @@ x1+x2+x3+x4,
 ```
 Polynomials may be multiline, thus `,` as a separator.
 
-Coefficients can be rational, using `/`, e.g. `-2/3*x2*y1^2+...`.
+Coefficients can be rational, using `/`, e.g. `-2/3*x2*y1^2+...`
+(leading rational form only: `1/2*x`, not `x/2`).
 
-In each polynomial, a single occurrence of each monomial is expected; the
-behaviour of msolve's parser is undefined if some monomial is repeated, as in
-`x1+x2+x3+x4-x1`.
+In each polynomial, a single occurrence of each monomial is expected.
+Parentheses, post-monomial division (`x/2`), a leading `*`, repeated
+monomials, and (over a prime field) coefficients that do not fit in a
+machine word are rejected with a nonzero exit code.
 
 # Basic usage
 
@@ -99,6 +101,10 @@ Using the `-g 2` flag as follows
 ```
 will return the reduced Groebner basis for the graded reverse 
 lexicographic ordering.
+Over a prime field this is exact. Over the rationals, coefficients are
+lifted to Q when possible; if lifting is skipped (in particular when the
+basis is `{1}`, or when only leading monomials are requested with `-g 1`)
+the header prints the first modular prime rather than characteristic 0.
 
 `msolve` also allows you to perform Groebner bases computations using 
 **one-block elimination monomial order**

input_files/bad-div.ms

@@ -0,0 +1,4 @@
+x, y
+0
+x/2 - y,
+y - 3

input_files/bad-overflow-ff.ms

@@ -0,0 +1,3 @@
+x
+65521
+9223372036854775808*x

input_files/bad-paren.ms

@@ -0,0 +1,3 @@
+x
+0
+x-(3+1)

input_files/bad-star.ms

@@ -0,0 +1,3 @@
+x
+0
+*x

input_files/good-leading-rat.ms

@@ -0,0 +1,3 @@
+x
+0
+1/2*x-1

output_files/empty-elim-qq.g2.e2.res

@@ -1,6 +1,7 @@
 #Reduced Groebner basis data
 #---
-#field characteristic: 0
+#field characteristic: <unlifted prime>
+#lifted to Q:          no (first modular prime only)
 #variable order:       z
 #monomial order:       graded reverse lexicographical
 #length of basis:      0 elements sorted by increasing leading monomials

output_files/good-leading-rat.g2.res

@@ -0,0 +1,8 @@
+#Reduced Groebner basis data
+#---
+#field characteristic: 0
+#variable order:       x
+#monomial order:       graded reverse lexicographical
+#length of basis:      1 element
+#---
+[x-2]:

output_files/one-qq.g2.res

@@ -1,6 +1,7 @@
 #Reduced Groebner basis data
 #---
-#field characteristic: 0
+#field characteristic: <unlifted prime>
+#lifted to Q:          no (first modular prime only)
 #variable order:       x, y, z
 #monomial order:       graded reverse lexicographical
 #length of basis:      1 element