gh-38365: add access to printlevel in libsingular

    
this is adding and using a simplified access to libsingular
``printlevel`` state variable

useful in turning down the comments easily

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.
    
URL: #38365
Reported by: Frédéric Chapoton
Reviewer(s): Kwankyu Lee

src/sage/libs/singular/decl.pxd

@@ -425,6 +425,7 @@ cdef extern from "singular/Singular/libsingular.h":
     cdef int si_opt_2    #  previously 'verbose'
     cdef void * currentVoice
     cdef int myynest
+    cdef int printlevel
 
     ctypedef char * const_char_ptr "const char *"
     cdef extern void (*WerrorS_callback)(const_char_ptr)

src/sage/libs/singular/function.pyx

@@ -1823,6 +1823,45 @@ def lib(name):
         raise NameError("Singular library {!r} not found".format(name))
 
 
+def get_printlevel():
+    """
+    Return the value of the variable ``printlevel``.
+
+    This is useful to switch off and back the comments.
+
+    EXAMPLES::
+
+        sage: from sage.libs.singular.function import get_printlevel, set_printlevel
+        sage: l = get_printlevel()
+        sage: set_printlevel(-1)
+        sage: get_printlevel()
+        -1
+        sage: set_printlevel(l)
+    """
+    global printlevel
+    cdef int pl = printlevel
+    return pl
+
+
+def set_printlevel(l):
+    """
+    Set the  value of the variable ``printlevel``.
+
+    This is useful to switch off and back the comments.
+
+    EXAMPLES::
+
+        sage: from sage.libs.singular.function import get_printlevel, set_printlevel
+        sage: l = get_printlevel()
+        sage: set_printlevel(2)
+        sage: get_printlevel()
+        2
+        sage: set_printlevel(l)
+    """
+    global printlevel
+    printlevel = <int>l
+
+
 def list_of_functions(packages=False):
     """
     Return a list of all function names currently available.

src/sage/rings/function_field/function_field_polymod.py

@@ -2380,22 +2380,17 @@ def _singular_normal(ideal):
         sage: _singular_normal(ideal(f))
         [[1]]
     """
-    from sage.libs.singular.function import singular_function, lib
-    lib('normal.lib')
+    from sage.libs.singular.function import (singular_function,
+                                             lib as singular_lib,
+                                             get_printlevel, set_printlevel)
+    singular_lib('normal.lib')
     normal = singular_function('normal')
-    execute = singular_function('execute')
 
-    try:
-        get_printlevel = singular_function('get_printlevel')
-    except NameError:
-        execute('proc get_printlevel {return (printlevel);}')
-        get_printlevel = singular_function('get_printlevel')
-
-    # It's fairly verbose unless printlevel is -1.
+    # verbose unless printlevel is -1.
     saved_printlevel = get_printlevel()
-    execute('printlevel=-1')
+    set_printlevel(-1)
     nor = normal(ideal)
-    execute('printlevel={}'.format(saved_printlevel))
+    set_printlevel(saved_printlevel)
 
     return nor[1]
 

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -5837,20 +5837,17 @@ cdef class MPolynomial_libsingular(MPolynomial_libsingular_base):
         """
         R = self.parent()
         algorithm = algorithm.lower()
-        from sage.libs.singular.function import singular_function, lib as singular_lib
+        from sage.libs.singular.function import (singular_function,
+                                                 get_printlevel,
+                                                 set_printlevel,
+                                                 lib as singular_lib)
         singular_lib('algebra.lib')
         if algorithm == "algebra_containment":
-            execute = singular_function('execute')
-            try:
-                get_printlevel = singular_function('get_printlevel')
-            except NameError:
-                execute('proc get_printlevel {return (printlevel);}')
-                get_printlevel = singular_function('get_printlevel')
-            # It's fairly verbose unless printlevel is -1.
+            # verbose unless printlevel is -1.
             saved_printlevel = get_printlevel()
-            execute('printlevel=-1')
+            set_printlevel(-1)
             contains = singular_function('algebra_containment')(self, R.ideal(J)) == 1
-            execute('printlevel={}'.format(saved_printlevel))
+            set_printlevel(saved_printlevel)
             return contains
         elif algorithm == "insubring":
             return singular_function('inSubring')(self, R.ideal(J))[0] == 1

src/sage/schemes/curves/projective_curve.py

@@ -141,6 +141,7 @@
 from sage.categories.fields import Fields
 from sage.categories.homset import hom, Hom, End
 from sage.categories.number_fields import NumberFields
+from sage.libs.singular.function import singular_function, lib as singular_lib, get_printlevel, set_printlevel
 from sage.matrix.constructor import matrix
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
@@ -1662,10 +1663,18 @@ def is_complete_intersection(self):
             sage: C.is_complete_intersection()
             False
         """
-        singular.lib("sing.lib")
-        id = singular.simplify(self.defining_ideal(), 10)
-        L = singular.is_ci(id).sage()
-        return len(self.ambient_space().gens()) - len(id.sage().gens()) == L[-1]
+        singular_lib("sing.lib")
+        simplify = singular_function("simplify")
+        is_ci = singular_function("is_ci")
+
+        # verbose unless printlevel is -1.
+        saved_printlevel = get_printlevel()
+        set_printlevel(-1)
+        id = simplify(self.defining_ideal(), 10)
+        L = is_ci(id)[-1]
+        set_printlevel(saved_printlevel)
+
+        return len(self.ambient_space().gens()) - len(id) == L
 
     def tangent_line(self, p):
         """
@@ -1860,11 +1869,13 @@ def rational_parameterization(self):
             raise TypeError("this curve must have geometric genus zero")
         if not isinstance(self.base_ring(), RationalField):
             raise TypeError("this curve must be defined over the rational field")
+
         singular.lib("paraplanecurves.lib")
-        R = singular.paraPlaneCurve(self.defining_polynomial())
-        singular.setring(R)
-        param = singular('PARA').sage().gens()
+        R = singular.paraPlaneCurve(self.defining_polynomial())  # ring
+        R.set_ring()
+        param = singular('PARA').sage().gens()  # ideal
         R = R.sage()
+
         C = self.change_ring(R.base_ring())
         H = Hom(ProjectiveSpace(R.base_ring(), 1, R.gens()), C)
         return H(param)
@@ -2043,7 +2054,7 @@ def _points_via_singular(self, sort=True):
 
         X2 = singular.NSplaces(1, X1)
         R = X2[5][1][1]
-        singular.set_ring(R)
+        R.set_ring()
 
         # We use sage_flattened_str_list since iterating through
         # the entire list through the sage/singular interface directly
@@ -2127,7 +2138,7 @@ def riemann_roch_basis(self, D):
         pnts = [(int(v[i][0]), int(v[i][2])-1) for i in range(len(v))]
         # retrieve coordinates of rational points
         R = X2[5][1][1]
-        singular.set_ring(R)
+        R.set_ring()
         v = singular('POINTS').sage_flattened_str_list()
         coords = [self(int(v[3*i]), int(v[3*i+1]), int(v[3*i+2])) for i in range(len(v)//3)]
         # build correct representation of D for singular