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, Variable
from proveit.linear_algebra import Norm
from proveit.numbers import Abs, Exp, Mult, Neg, e, i, one, pi, two
from proveit.physics.quantum import ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Norm(ket1)
expr = ExprTuple(Mult(Abs(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase))), sub_expr1), Mult(one, sub_expr1))

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|\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi}\right| \cdot \left \|\lvert 1 \rangle\right \|, 1 \cdot \left \|\lvert 1 \rangle\right \|\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: 19 operands: 3
2	Operation	operator: 19 operands: 4
3	ExprTuple	5, 6
4	ExprTuple	18, 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operand: 12
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Operation	operator: 25 operands: 13
12	Operation	operator: 14 operand: 18
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18
16	Literal
17	Operation	operator: 19 operands: 20
18	Literal
19	Literal
20	ExprTuple	27, 21, 22, 23, 24
21	Literal
22	Literal
23	Operation	operator: 25 operands: 26
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	Variable