# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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 e
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Neg, one, subtract
from proveit.physics.quantum.QPE import _neg_domain, _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
expr = Equals(_neg_domain, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} = \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 1\}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple9, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 30
operand: 14
9Operationoperator: 26
operands: 12
10Operationoperator: 26
operands: 13
11ExprTuple14
12ExprTuple15, 32
13ExprTuple16, 29
14Operationoperator: 26
operands: 17
15Operationoperator: 30
operand: 20
16Operationoperator: 30
operand: 21
17ExprTuple21, 32
18ExprTuple20
19ExprTuple21
20Operationoperator: 22
operands: 23
21Variable
22Literal
23ExprTuple24, 25
24Literal
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28, 29
28Literal
29Operationoperator: 30
operand: 32
30Literal
31ExprTuple32
32Literal