FEAT: implement use_coefficients switch

[redeboer]

Closes #156

This PR makes it possible to combine the product of the two couplings into one scaling coefficient, by writing use_coefficients=True in the DalitzPlotDecompositionBuilder.formulate()

[redeboer]

@Zeyna777 I still need to write some unit tests for this. However, you can already try it, for instance on 15b3807 like this:

uv add git+https://github.com/ComPWA/ampform-dpd --rev 15b3807

[redeboer]

@mmikhasenko here are the number I was referring to:

ampform-dpd/tests/test_dpd_builder.py

Lines 82 to 148 in 9d75497

	# ----==== COEFFICIENTS ===--- #
	if use_coefficients:
	if min_ls: # HELICITY BASIS
	assert n_coupling_symbols == 20
	assert coupling_symbols_str == [
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-1/2, -1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-1/2, -1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-1/2, 1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-1/2, 1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-3/2, -1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[-3/2, -1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[1/2, -1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[1/2, -1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[1/2, 1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[1/2, 1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[3/2, 1/2, 0, -1/2]",
	R"\mathcal{H}^\mathrm{N(1700)^{+}}[3/2, 1/2, 0, 1/2]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[-1/2, -1/2, -1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[-1/2, -1/2, 1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[-1/2, 1/2, -1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[-1/2, 1/2, 1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[1/2, -1/2, -1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[1/2, -1/2, 1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[1/2, 1/2, -1/2, 0]",
	R"\mathcal{H}^\mathrm{\overline{\Sigma}(1660)^{-}}[1/2, 1/2, 1/2, 0]",
	]
	else: # CANONICAL BASIS
	assert n_coupling_symbols == 4
	assert coupling_symbols_str == [
	R"\mathcal{H}^\mathrm{LS,N(1700)^{+}}[1, 1, 2, 1/2]",
	R"\mathcal{H}^\mathrm{LS,N(1700)^{+}}[1, 2, 2, 1/2]",
	R"\mathcal{H}^\mathrm{LS,\overline{\Sigma}(1660)^{-}}[0, 1, 1, 1/2]",
	R"\mathcal{H}^\mathrm{LS,\overline{\Sigma}(1660)^{-}}[2, 1, 1, 1/2]",
	]
	# ----==== COUPLING ===--- #
	else:
	n_products = len(_collect_products(amplitudes))
	if min_ls: # HELICITY BASIS
	assert n_coupling_symbols == 14
	assert n_products == 20
	assert coupling_symbols_str == [
	R"\mathcal{H}^\mathrm{decay}[N(1700)^{+}, 0, -1/2]",
	R"\mathcal{H}^\mathrm{decay}[N(1700)^{+}, 0, 1/2]",
	R"\mathcal{H}^\mathrm{decay}[\overline{\Sigma}(1660)^{-}, -1/2, 0]",
	R"\mathcal{H}^\mathrm{decay}[\overline{\Sigma}(1660)^{-}, 1/2, 0]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, -1/2, -1/2]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, -1/2, 1/2]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, -3/2, -1/2]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, 1/2, -1/2]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, 1/2, 1/2]",
	R"\mathcal{H}^\mathrm{production}[N(1700)^{+}, 3/2, 1/2]",
	R"\mathcal{H}^\mathrm{production}[\overline{\Sigma}(1660)^{-}, -1/2, -1/2]",
	R"\mathcal{H}^\mathrm{production}[\overline{\Sigma}(1660)^{-}, -1/2, 1/2]",
	R"\mathcal{H}^\mathrm{production}[\overline{\Sigma}(1660)^{-}, 1/2, -1/2]",
	R"\mathcal{H}^\mathrm{production}[\overline{\Sigma}(1660)^{-}, 1/2, 1/2]",
	]
	else: # CANONICAL BASIS
	assert n_coupling_symbols == 6
	assert n_products == 4
	assert coupling_symbols_str == [
	R"\mathcal{H}^\mathrm{LS,decay}[N(1700)^{+}, 2, 1/2]",
	R"\mathcal{H}^\mathrm{LS,decay}[\overline{\Sigma}(1660)^{-}, 1, 1/2]",
	R"\mathcal{H}^\mathrm{LS,production}[N(1700)^{+}, 1, 1]",
	R"\mathcal{H}^\mathrm{LS,production}[N(1700)^{+}, 1, 2]",
	R"\mathcal{H}^\mathrm{LS,production}[\overline{\Sigma}(1660)^{-}, 0, 1]",
	R"\mathcal{H}^\mathrm{LS,production}[\overline{\Sigma}(1660)^{-}, 2, 1]",
	]

This is the corresponding decay:

ampform-dpd/tests/conftest.py

Lines 28 to 31 in 7af7d3c

	initial_state=[("J/psi(1S)", [+1])],
	final_state=["K0", ("Sigma+", [+0.5]), ("p~", [+0.5])],
	allowed_interaction_types="strong",
	allowed_intermediate_particles=["N(1700)+", "Sigma(1660)"],

[redeboer]

You're right: the number of coupling products (aka coefficients) is simply $n_\text{product} \cdot n_\text{decay}$