# 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.
# import Expression classes needed to build the expression
from proveit import e
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Neg(Mult(frac(one, Exp(two, one)), _two_pow_t))

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())

\left(e - \left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1 - e\right) = \left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 1\right)

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
5ExprTuple13, 9, 27, 8
6Literal
7ExprTuple9, 27
8Operationoperator: 11
operand: 13
9Operationoperator: 11
operand: 14
10ExprTuple13
11Literal
12ExprTuple14
13Variable
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Operationoperator: 19
operands: 20
18Operationoperator: 24
operands: 21
19Literal
20ExprTuple27, 22
21ExprTuple26, 23
22Operationoperator: 24
operands: 25
23Literal
24Literal
25ExprTuple26, 27
26Literal
27Literal