Guard PARI polgalois on unsupported number-field degrees

lmfdb/number_fields/code.yaml

@@ -156,7 +156,7 @@ class_number_formula:
 galois_group:
   comment: Galois group
   sage:  K.galois_group()
-  pari:  polgalois(K.pol)
+  pari:  'if(poldegree(K.pol) > 11, "polgalois only supports degree <= 11", iferr(polgalois(K.pol), E, "polgalois in degrees 8 to 11 requires the optional galdata package", errname(E) == "e_FILE" || errname(E) == "e_PACKAGE"))'
   magma: GaloisGroup(K);
   oscar: |
     G, Gtx = galois_group(K);

lmfdb/number_fields/test_numberfield.py

@@ -185,3 +185,24 @@ def test_signature_download(self):
         # Also ensure we're not getting quoted strings
         assert '"[0, 1]"' not in page
         assert '"[2, 0]"' not in page
+
+    def test_high_degree_gp_galois_download(self):
+        # PARI's polgalois hard-errors above degree 11, and needs the optional
+        # galdata package in degrees 8 to 11, so the snippet must be guarded.
+        # The committed gp snippet logs only exercise degrees 1 and 2, i.e. the
+        # branch where polgalois is actually called.
+        page = self.tc.get('/NumberField/12.4.320979616137216.3/download/gp').get_data(as_text=True)
+        assert 'poldegree(K.pol) > 11' in page
+        assert 'polgalois only supports degree <= 11' in page
+        assert 'requires the optional galdata package' in page
+        # polgalois is never invoked from an unguarded line
+        assert not any(line.strip() == 'polgalois(K.pol)' for line in page.split('\n'))
+
+    def test_rational_field_magma_download(self):
+        # Magma's NumberField collapses a degree 1 polynomial to the rationals,
+        # so 1.1.1.1 uses RationalsAsNumberField() instead, both when defining
+        # the field and in the self-contained class number formula snippet.
+        page = self.tc.get('/NumberField/1.1.1.1/download/magma').get_data(as_text=True)
+        assert page.count('K<a> := RationalsAsNumberField();') == 2
+        assert 'NumberField(x)' not in page
+        assert 'DoLinearExtension' not in page

lmfdb/tests/snippet_tests/number_fields/code-1.1.1.1-gp.log

@@ -30,7 +30,7 @@ gp> [polcoeff (lfunrootres (lfuncreate (K))[1][1][2], -1), 2^K.r1 * (2*Pi)^K.r2
 [1.0000000000000000000000000000000000000, 1.0000000000000000000000000000000000000]
 gp> L = nfsubfields(K); L[2..length(L)]
 []
-gp> polgalois(K.pol)
+gp> if(poldegree(K.pol) > 11, "polgalois only supports degree <= 11", iferr(polgalois(K.pol), E, "polgalois in degrees 8 to 11 requires the optional galdata package", errname(E) == "e_FILE" || errname(E) == "e_PACKAGE"))
 [1, 1, 1, "S1"]
 gp> p = 7; pfac = idealprimedec(K, p); vector(length(pfac), j, [pfac[j][3], pfac[j][4]])
 [[1, 1]]

lmfdb/tests/snippet_tests/number_fields/code-2.0.4.1-gp.log

@@ -30,7 +30,7 @@ gp> [polcoeff (lfunrootres (lfuncreate (K))[1][1][2], -1), 2^K.r1 * (2*Pi)^K.r2
 [0.78539816339744830961566084581987572105, 0.78539816339744830961566084581987572105]
 gp> L = nfsubfields(K); L[2..length(L)]
 [[x^2 + 1, x]]
-gp> polgalois(K.pol)
+gp> if(poldegree(K.pol) > 11, "polgalois only supports degree <= 11", iferr(polgalois(K.pol), E, "polgalois in degrees 8 to 11 requires the optional galdata package", errname(E) == "e_FILE" || errname(E) == "e_PACKAGE"))
 [2, -1, 1, "S2"]
 gp> p = 7; pfac = idealprimedec(K, p); vector(length(pfac), j, [pfac[j][3], pfac[j][4]])
 [[1, 2]]