making a new module for acb_theta

Author: edgarcosta

meson.build

@@ -22,6 +22,9 @@ endif
 # flint.pc was missing -lflint until Flint 3.1.0
 if flint_dep.version().version_compare('<3.1')
   flint_dep = cc.find_library('flint')
+  have_acb_theta = false
+else
+  have_acb_theta = true
 endif
 
 pyflint_deps = [dep_py, gmp_dep, mpfr_dep, flint_dep]

src/flint/types/acb_mat.pyx

@@ -19,7 +19,6 @@ from flint.flintlib.arb_mat cimport *
 from flint.flintlib.arf cimport *
 from flint.flintlib.acb cimport *
 from flint.flintlib.acb_mat cimport *
-from flint.flintlib.acb_theta cimport *
 
 cimport cython
 
@@ -818,47 +817,18 @@ cdef class acb_mat(flint_mat):
 
     def theta(tau, z, square=False):
         r"""
-        Computes the vector valued Riemann theta function `(\theta_{a,b}{z, tau) : a, b \in \{0,1\}^{g}\)` or its squares.
-        This is a wrapper for the function `acb_theta_all` and it follows the same conventions for the ordering of the theta characteristics.
-
-            >>> from flint import acb, acb_mat, showgood
-            >>> z = acb(1+1j); tau = acb(1.25+3j)
-            >>> t0, t1, t2, t3 = acb_mat([[tau]]).theta(acb_mat([[z]]))
-            >>> sum([abs(x) for x in acb_mat([z.modular_theta(tau)]) - acb_mat([[-t3,t2,t0,t1]])])
-            [+/- 3.82e-14]
-            >>> for i in range(4):showgood(lambda: acb_mat([[tau]]).theta(acb_mat([[z]]))[i], dps=25)
-            ...
-            0.9694430387796704100046143 - 0.03055696120816803328582847j
-            1.030556961196006476576271 + 0.03055696120816803328582847j
-            -1.220790267576967690128359 - 1.827055516791154669091679j
-            -1.820235910124989594900076 + 1.216251950154477951760042j
-            >>> acb_mat([[1j,0],[0,2*1j]]).theta(acb_mat([[0],[0]]))
-            ([1.09049252082308 +/- 3.59e-15] + [+/- 2.43e-16]j, [1.08237710165638 +/- 4.15e-15] + [+/- 2.43e-16]j, [0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j, [0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j, [0.451696791791346 +/- 5.46e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j, [0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j)
-
-        """
-        g = tau.nrows()
-        assert tau.ncols() == g
-        assert z.nrows() == g
-        assert z.ncols() == 1
-
-        # convert input
-        cdef acb_ptr zvec
-        zvec = _acb_vec_init(g)
-        cdef long i
-        for i in range(g):
-            acb_set(zvec + i, acb_mat_entry((<acb_mat>z).val, i, 0))
-
-        # initialize the output
-        cdef slong nb = 1 << (2 * g)
-        cdef acb_ptr theta = _acb_vec_init(nb)
-
-        acb_theta_all(theta, zvec, tau.val, square, getprec())
-        _acb_vec_clear(zvec, g)
-        # copy the output
-        res = tuple()
-        for i in range(nb):
-            r = acb.__new__(acb)
-            acb_set((<acb>r).val, theta + i)
-            res += (r,)
-        _acb_vec_clear(theta, nb)
-        return res
+        Computes the vector valued Riemann theta function
+        `(\theta_{a,b}{z, tau) : a, b \in \{0,1\}^{g}\)` or its squares.
+        This is a wrapper for the C-function `acb_theta_all` and it follows the
+        same conventions for the ordering of the theta characteristics.
+
+        This is a wrapper for :meth:`.acb_theta.acb_mat_theta`; see the
+        documentation for that method for details for examples.
+        """
+        try:
+            from .acb_theta import acb_mat_theta
+        except ImportError:
+            acb_mat_theta = None
+        if acb_mat_theta is None:
+            raise NotImplementedError("acb.theta() needs Flint >= 3.1.0")
+        return acb_mat_theta(z, tau, square=square)

src/flint/types/acb_theta.pyx

@@ -0,0 +1,56 @@
+from flint.flint_base.flint_context cimport getprec
+from flint.types.acb cimport acb
+from flint.types.acb_mat cimport acb_mat
+from flint.flintlib.acb cimport *
+from flint.flintlib.acb_mat cimport *
+from flint.flintlib.acb_theta cimport *
+
+def acb_mat_theta(acb_mat z, acb_mat tau, ulong square=False):
+    r"""
+    Computes the vector valued Riemann theta function `(\theta_{a,b}{z, tau) : a, b \in \{0,1\}^{g}\)` or its squares.
+    This is a wrapper for the function `acb_theta_all` and it follows the same conventions for the ordering of the theta characteristics.
+
+    This should be used via method `acb_mat.theta` with the order of `z` and `tau` swapped,
+
+        >>> from flint import acb, acb_mat, showgood
+        >>> z = acb(1+1j); tau = acb(1.25+3j)
+        >>> t0, t1, t2, t3 = acb_mat([[tau]]).theta(acb_mat([[z]]))
+        >>> sum([abs(x) for x in acb_mat([z.modular_theta(tau)]) - acb_mat([[-t3,t2,t0,t1]])])
+        [+/- 3.82e-14]
+        >>> for i in range(4):showgood(lambda: acb_mat([[tau]]).theta(acb_mat([[z]]))[i], dps=25)
+        ...
+        0.9694430387796704100046143 - 0.03055696120816803328582847j
+        1.030556961196006476576271 + 0.03055696120816803328582847j
+        -1.220790267576967690128359 - 1.827055516791154669091679j
+        -1.820235910124989594900076 + 1.216251950154477951760042j
+        >>> acb_mat([[1j,0],[0,2*1j]]).theta(acb_mat([[0],[0]]))
+        ([1.09049252082308 +/- 3.59e-15] + [+/- 2.43e-16]j, [1.08237710165638 +/- 4.15e-15] + [+/- 2.43e-16]j, [0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j, [0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j, [0.451696791791346 +/- 5.46e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.916991251621117 +/- 6.30e-16] + [+/- 2.43e-16]j, [0.910167024735558 +/- 7.93e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [0.379830212998946 +/- 4.47e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j, [+/- 2.43e-16] + [+/- 2.43e-16]j)
+
+    """
+    g = tau.nrows()
+    assert tau.ncols() == g
+    assert z.nrows() == g
+    assert z.ncols() == 1
+
+    # convert input
+    cdef acb_ptr zvec
+    zvec = _acb_vec_init(g)
+    cdef long i
+    for i in range(g):
+        acb_set(zvec + i, acb_mat_entry(z.val, i, 0))
+
+    # initialize the output
+    cdef slong nb = 1 << (2 * g)
+    cdef acb_ptr theta = _acb_vec_init(nb)
+
+    acb_theta_all(theta, zvec, tau.val, square, getprec())
+    _acb_vec_clear(zvec, g)
+    # copy the output
+    res = tuple()
+    cdef acb r
+    for i in range(nb):
+        r = acb.__new__(acb)
+        acb_set(r.val, theta + i)
+        res += (r,)
+    _acb_vec_clear(theta, nb)
+    return res

src/flint/types/meson.build

@@ -41,6 +41,10 @@ exts = [
   'fmpz_mpoly',
 ]
 
+if have_acb_theta
+  exts += ['acb_theta']
+endif
+
 py.install_sources(
   pyfiles,
   pure: false,