Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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 ExprTuple
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum.QPE import _U, _ket_u, _phase

# build up the expression from sub-expressions
expr = ExprTuple(MatrixMult(_U, _ket_u), ScalarMult(Exp(e, Mult(two, pi, i, _phase)), _ket_u))

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(U \thinspace \lvert u \rangle, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 9
5	Literal
6	ExprTuple	8, 9
7	Literal
8	Operation	operator: 10 operands: 11
9	Literal
10	Literal
11	ExprTuple	12, 13
12	Literal
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17, 18, 19
16	Literal
17	Literal
18	Literal
19	Literal