Expression of type And

from the theory of proveit.physics.quantum.circuits

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, IndexedVar, U, Variable, t
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import And, Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import var_ket_u, varphi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, Equals(MatrixMult(IndexedVar(U, sub_expr1), var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, IndexedVar(varphi, sub_expr1))), var_ket_u)), one, t))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(U_{1} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert u \rangle\right)\right) \land  \left(\left(U_{2} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert u \rangle\right)\right) \land  \ldots \land  \left(\left(U_{t} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{t}} \cdot \lvert u \rangle\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3
3	ExprRange	lambda_map: 4 start_index: 5 end_index: 6
4	Lambda	parameter: 32 body: 7
5	Literal
6	Variable
7	Operation	operator: 8 operands: 9
8	Literal
9	ExprTuple	10, 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 18
14	Literal
15	ExprTuple	17, 18
16	IndexedVar	variable: 19 index: 32
17	Operation	operator: 20 operands: 21
18	Variable
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27, 28, 29
26	Literal
27	Literal
28	Literal
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable